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IB12) 



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In course of publication, in BHffll 8vo. each, volume containing about 300 pages, price 
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SERIES OIF 

ELEMENTARY WORKS OS MECHANICAL AID 
PHYSICAL SCIEICE, 



FORMING A SERIES OF 



TEXT-BOOKS OF SCIENCE, 

ADAPTED FOR THE USE OP ARTISANS AND OP STUDENTS IN 
PUBLIC AND OTHER SCHOOLS. 



The first Eight Text-Books, in order of publication .— 

I. THE ELEMENTS OF MECHANISM, 

Designed for Students of Applied Mechanics. By T. M. Goodeve, MA. 
Lecturer on Applied Mechanics at the Royal School of Mines, and formerly 
Professor of Natural Philosophy in King's College, London. New Edition, 
revised ; with 257 Figures on Wood. Price 3s. 6d. 

II. METALS, THEIR PROPERTIES AND TREATMENT. 

By Charles Loudon Bloxam, Professor of Chemistry in King's College, 
London ; Professor of Chemistry in the Department of Artillery Studies, and 
in the Royal Military Academy, Woolwich. With 105 Figures on Wood. 
Price 3s. Gd. 

III. INTRODUCTION TO THE STUDY OF INORGANIC 

CHEMISTRY. 

By William Allen Miller, MJD. LL.D. F.R.S. late Professor of Chemistry 
in King's College, London ; Author of ' Elements of Chemistry, Theoretica 
and Practical.' New Edition, revised ; with 71 Figures on Wood. Price 3s. Qd 

IV. ALGEBRA AND TRIGONOMETRY. 

By the Rev. William Nathaniel Griffin, B.D. sometime Fellow of 
St. John's College, Cambridge. Price 3s. 6c?. 

NOTES ON THE ' ELEMENTS OF ALGEBRA AND TRIGO 
NOMETRY'; 

With SOLUTIONS of the more Difficult QUESTIONS. By the Rev. 
W. N. Griffin, B.D. Sometime Fellow of St. John's College, Cambridge. 

[Nearly ready. 

V. PLANE AND SOLID GEOMETRY. 

By the Rev. H. W. Watson, formerly Fellow of Trinity College, Cambridge, 
and late Assistant-Master of Harrow School. Price 3s. 6d. 

VI. THEORY OF HEAT. 

By J. Clerk Maxwell, MA. LL.D. Edin. F.R.SS. L. & E. Professor of 
Experimental Physics in the University of Cambridge. New Edition, revised ; 
with 41 Woodcuts and Diagrams. Price 3s. 6d. 

VII. TECHNICAL ARITHMETIC AND MENSURATION. 

By Charles W. Merrifield, F.R.S. Barrister-at-Law, Principal of the Royal 
School of Naval Architecture and Marine Engineering, Honorary Secretary' 
of the Institution of Naval Architects, and Late an Examiner in the Depart- 
ment of Public Education. Price 3s. 6d. 



Text-Books of Science — continued. 



VIII. THE STRENGTH OF MATERIALS AND STRUCTURES: 

The Strength of Materials as depending- on their quality and as ascertained 
by Testing Apparatus ; the Strength of Structures as depending on their 
form and arrangement, and on the Materials of which they are composed. 

By John Anderson, O.E. LL.D. F.T?S.E. Superintendent of Machinery 
to the War Department, Royal Arsenal, Woolwich. Price 3s. Gd. 

Text-Books in immediate preparation: — 
ORGANIC CHEMISTRY. 

By H. E. Armstrong, Ph.D. Professor of Chemistry in the London 

Institution. 

ELECTRICITY AND MAGNETISM. 

By Fleemino .Tentcin. F.R.SS. L. & E. Professor of Engineering in the 
University of Edinburgh. 

A MANUAL OF QUANTITATIVE ANALYSIS. 

Bv T. E. Thorpe, Ph.D. F.R.S.E. Professor of Chemistry in the Andersonian 
University, Glasgow. 

PRACTICAL AND DESCRIPTIVE GEOMETRY, AND PRIN- 
CIPLES OF MECHANICAL DRAWING. 

By Charles W. Merrifield, F.R.S. Barrister-at-Law, Principal of the Royal 
School of Naval Architecture and Marine Engineering. Honorary Secretary of 
th e Tr> stitntion of Naval' Architects, and lately an Examiner in the Department 
of Public Education. 

PRINCIPLES OF MECHANICS. 

Bv T. M. Goobeve, MA. "Lecturer on Applied Mechanics at the Royal School 
of Mines, and formerly Professor of Natural Philosophy in King's College, 
London. 

ELEMENTS OF MACHINE DESIGN. 

With Rules and Tables for Designing- and Drawing the Details of Machinery. 
Adapted to the use of Mechanical Draughtsmen and Teachers of Machine 
Drawine-. 

Bv W. Cawthorne Unwin. B.Sc. Assoc. Inst. C.E. Professor of Hydraulic 
and Mechanical Engineering at Cooper's Hill College. 

DESCRIPTIVE MECHANISM, 

Including Descriptions of the Lathes. Planing, Slotting, and Shaping 
Machines, and the mode of Handling Work in the Engineer's Shop and 
other Workshops. 

Bv c. P. B. Shelley, Civil Enarineer, and Professor of Manufacturing Art 
and Machinery at King's College, London. 

ECONOMICAL APPLICATIONS OF HEAT, 

Including Combustion, Evaporation, Furnaces, Flues, and Boilers. 

By C. P. B. Shelley, Civil Engineer, and Professor of Manufacturing 
Art and Machinery at King's College, London. 
With a Chapter on the Probable Future Development of the Science of Heat, by 
C. William Siemens, F.R.S. 

THE STEAM ENGINE. 

By T. M. Goobeve, MA. Lecturer on Applied Mechanics at the Royal School 
of Mines, and formerly Professor. of Natural Philosophy in King's College, 
London. 

SOUND AND LIGHT. 

By G. G. Stokes, M.A. D.C.L. Fellow of Pembroke College, Cambridge; 
Lucasian Professor of Mathematics in the University of Cambridge; and 
Secretary to the Royal Society. 

*** To be followed by other works on other branches of Science. 



London: LONGMANS and CO. Paternoster Row. 






y ^f< 1876 \ 

> REC'D DEC oo , I 

TEXT-BOOKS OF SCIENCE 




ADAPTED FOR THE USE OF 



ARTISANS AND STUDENTS IN PUBLIC AND OTHER SCHOOLS. 



THE STRENGTH OF MATERIALS 
AND STRUCTURES. 




Transfer 

Armv War College 

June 20 1933 



THE 



STRENGTH OF MATERIALS 
AND STRUCTURES. 



PART I. 

THE STRENGTH OF MATERIALS, AS DEPENDING ON 
THEIR QUALITY, AND AS ASCERTAINED BY 
TESTING - APPARA TUS. 

PART II. 

THE STRENGTH OF STRUCTURES, AS DEPENDING ON 
THE FORM AND ARRANGEMENT OF THEIR PARTS, 
AND ON THE MATERIALS OF WHICH THEY ARE 
CONSTRUCTED. 



BY 

JOHN ANDERSON, C.E. LL.D. F.R.S.E. 

r« 

Superintendent of Machinery to the War Department ; formerly Lecturer 

071 Applied Mechanics at the Royal Military Academy, Woolwich; 

at the Royal Engineer Establishment, Chathavt ; and at the 

Royal School of Naval Architecture, South Kensington. 



D. APPLETON AND CO. 

549 & 551 BROADWAY, 

NEW YORK. 

1872. 



T/Ho5 

I BIZ 




This Elementary Treatise is divided into two distinct 
parts. 

The First Part treats of the natural properties of various 
materials employed in construction, more especially in 
regard to their strength and elasticity, and their adapta- 
tion for particular practical purposes in the arts. The 
object of this portion of the work is to describe the qualities 
and characteristics of materials, so far as they are of impor- 
tance to the engineer, or are exhibited in the results of 
experiments made with the testing-machine. 

An acquaintance with the natural properties of materials, 
as forming part of the great field of applied mechanics, 
is indispensably necessary for the young mechanic or engi- 
neer, who desires to be something more than an artisan. 
That real knowledge, which consists in understanding the 
materials which he handles, and in a familiarity with their 
points of agreement or difference, both in regard to elas- 
ticity and strength, cannot fail to give a charm to his daily 
duty. 

As it cannot be expected that all will have the oppor- 
tunity of making experiments for themselves, the first three 
chapters are devoted to the testing of materials, and to the 
practical manipulation of a testing-machine. In these 
chapters reference is made to the physical properties of 



vi Preface. 

some common materials, by which the student will be able 
to comprehend the nature of such experimental inves- 
tigations, and the labour and care needed in order to arrive 
at true results ; and it is hoped that he will find the subject 
treated in such a clear and simple manner, that he may 
understand it without much difficulty. 

The fourth, fifth, sixth, seventh, and eighth chapters 
refer more especially to cast iron, wrought iron, steel, 
copper, alloys, and timber, and are intended to describe 
their qualities and leading peculiarities. 

The ninth, tenth, and eleventh chapters treat, more gene- 
rally, of the resistance of materials to torsion, shearing, and 
punching, and to transverse strains, conjoined with impact 
and vibration. 

The first eleven chapters, therefore, have regard to the 
nature of materials, and the remaining six chapters — which 
constitute the second part of the volume — are devoted 
to the strength of structures, when made of the materials 
previously treated of. 

In the Second Part, the student will learn the correct 
forms which must be given to the various structures in 
order to obtain the requisite strength, and likewise the best 
arrangement of materials, as depending on their respective 
properties, so that by the practical application of correct 
principles, the maximum of strength may be attained with 
the, minimum of weight and cost. 

The experiments most frequently referred to, and which 
are quoted as ' Woolwich experiments,' have all been made 
in the Royal Arsenal for various purposes during the past 
eighteen years, and chiefly with the American testing- 
machine, which is described in the third chapter, the only 
exception being certain experiments, to ascertain the strength 



Preface. vii 

of ropes under various conditions, which were carried out 
with a hydraulic testing-machine, recently transferred from 
Her Majesty's Dockyard to the Royal Arsenal. 

The author has taken pains to ensure accuracy ; still, when 
so many figures have been necessarily transcribed several 
times, more particularly in the Tables, some errors may 
probably exist. In this part of the work Mr. Charles Topple 
and Mr. George Cuthbert have both rendered valuable 
assistance; the former, more especially, in regard to the 
chapters on structures, where calculations were concerned. 
Most of the examples given are taken from actual works, 
which have passed through the author's hands during the 
past few years. 

The sources from whence the results of other experiments 
have been drawn, or from which extracts have been made, 
are generally quoted. Reference has very frequently been 
made to the Blue Book, containing the Report of the 
Commissioners appointed to enquire into the Application 
of Iron to Railway Structures. 

Woolwich : August 1872. 



CONTENTS. 



PART I. 

ON THE STRENGTH OF MATERIALS EMPLOYED IN 
CONSTRUCTION. 

CHAPTER I. 

ON SOME OF THE PHYSICAL PROPERTIES OF MATERIALS. 

Fitness of Materials for Special Purposes. Rigidity only apparent. 
Elasticity. Hooke's Law. Solids, Plastic Substances, Liquids and 
Gases. Permanent Set of Solids. Cases in which the Effects of 
Elasticity need to be counteracted .... Page i — 9 

CHAPTER II. 

ON THE EXPERIMENTAL TESTING OF MATERIALS. 

Need of Accuracy. Several Specimens should be tested. Stretching 
of Long and Short Specimens. Force to be applied in Axis of 
Specimen. Effect of Time. Limit of Elasticity. Form of Speci- 
mens. Testing Machines 9 — 15 

CHAPTER III. 

ON A MACHINE FOR TESTING THE STRENGTH AND ELASTICITY 
OF MATERIALS. 

Woolwich Machine. Balance of Machine. Application of Load. 
Construction of Specimen Holders. Behaviour of Specimens. Flow 
of Solids. Compressive Resistance. Transverse Resistance. Tor- 
sion. Deformation 15 — 29 



zi Contents. 

CHAPTER IV. 

CAST IRON. 

Production of Cast Iron. Influence of Carbon on Cast Iron. Mixing 
Cast Iron. Limit of Elasticity. Tenacity. Selection and Testing 
by Founder. Testing Girders. Woolwich Experiments. Experi- 
ments on io-feet Bars. Compressive Strength. Experiments on 
50-feet Bars. Woolwich Compressive Experiments. Remelted 
Iron. Strength at various Temperatures . . Page 30 — 45 

CHAPTER V. 

WROUGHT IRON. 

Production of Wrought Iron. Characteristics. Conditions determining 
Quality. Tenacity of Bars and Plates. Strength at high and low 
Temperatures. Appearance of Fracture. Effect of Vibration. 
Annealing. Safe Load. Red short and Cold short iron. Limit of 
Elasticity. Behaviour under Test of hard and ductile Specimens. 
Strength of Welds. Experiments on 50-feet Bars. Modulus of 
Elasticity. Compressive Resistance .... 46 — 67 

CHAPTER VI. 

STEEL. 

Production of Steel. Bessemer Steel. Effect of working. Whit- 
worth's Treatment. Mild Steel. Tempering in Oil. Strength of 
Steel. Tempering Barrels for Guns. Experiments on Steel. Com- 
pressive Resistance 68 — 76 

CHAPTER VII. 

ON COPPER AND OTHER METALS, AND THEIR ALLOYS. 

Copper. Its Tenacity. Forging. Effect of Exposure. Specific 
Gravity. Melting Point. Wiredrawing. ' Casting. Use of Phos- 
phorus. Experiments on Tenacity. Bronze and Gun-metal. 
Specific Gravity. Fusibility. Manufacture. Experiments on Gun- 
metal. Resistance to Tension and Compression. Brass. Manu- 
facture. Specific Gravity. Melting Point. Influence of Lead. 



Contents. xi 

Muntz Metal. Tensile Strength. Sterro-metal. Alumi- 
nium Bronze. Bell Metal. Babbitt's Metal. Melting Point 
of Alloys. Additional Experiments . . . Page 77 — 100 



CHAPTER VIII. 

TIMBER. 

Variability in Quality. Density. Conditions influencing Quality. 
Seasoning. Laws of Shrinkage. Ash. Beech. Elm. Pine and 
Fir. Hornbeam. Mahogany. Oak. Teak. Tensile and Com- 
pressive Resistance of Timber. Resistance to Shearing. Trans- 
verse Strength 101 — 121 



CHAPTER IX. 

TRANSVERSE STRENGTH OF IRON AND RESISTANCE TO 
IMPACT. 

Breaking Weight and Deflection of Bars. Effect of Impact. Trans- 
verse Flexure. Effect of repeated Deflections . . 122 — 130 

CHAPTER X. 

RESISTANCE TO TORSION AND SHEARING. 

Shafting. Law of Resistance to Twisting. Wrought and Cast Iron 
Shafting. Cast Steel and Copper under Torsion. Torsional Stiff- 
ness. Sudden Variations of Section. Experiments with Bars. Rup- 
ture by Torsion. Torsive Resistance of different Materials. Strength 
and Stiffness of Shafting. Resistance to Shearing and Punching. 
Gradual Shearing by inclined Instruments. Shearing Action on 
Links. Punching and Drilling . ... . . 130 — 149 



CHAPTER XI. 

ON THE IMPORTANCE OF UNIFORMITY OF SECTIONAL AREA. 

Surplus Material in parts a source of weakness. Screw Bolts. Chains. 
Proof Strains for Chains. Rules for Strength of Chains. Strength 
of Ropes. Rope Slings 149 — 156 



xii Contents. 



PART II. 

ON THE STRENGTH OF STRUCTURES. 

CHAPTER XII. 

BEAMS AND GIRDERS. 

Mathematics useful. Dependence on Formulae Beams and Girders.' 
Relative Strength as depending on Mode of Application of Load and 
Support. Strength as affected by Arrangement of Material. Neutral 
Surface. Tension and Compression in Beams. Flanged Girders. 
Rectangular Beams. Tubular Beams. Beams of uniform strength. 
Constants for Strength and Deflection of Beams. Cast and 
Wrought Iron Girders. Deflection of Beams. Resilience of 
Beams Page 157—187 

CHAPTER XIII. 

ON THE STRENGTH OF GEARING. 

Teeth of Wheels. Strength of Teeth. Flanging Wheel Teeth. 
Wear of Teeth. Wrought Iron Wheels. Malleable Cast Iron 
Wheels. Cast Steel Wheels. Power transmitted by Wheels. 
Strength of Screws. Cutting Instruments . . . 187 — 195 

CHAPTER XIV. 

ON THE STRENGTH OF LONG COLUMNS. 

Modes in which Columns yield. Short Columns. Euler's Theory. 
Hodgkinson's Experiments. Practical Deductions. Wrought Iron 
Columns. Cast Iron Columns. Strength of Rectangular and 
Cylindrical Tubes. Steel Shear Poles .... 195 — 206 



Contents. xiii 



CHAPTER XV. 

ON THE STRENGTH OF CRANES AND ROOF TRUSSES AS 
EXAMPLES OF COMPLEX STRUCTURES. 

Mode of dealing with Complex Structures. Bracing. Triangular 
arrangement of parts. Common Roof Truss. Trussed or Braced 
Girder. Stresses on Hydraulic Crane. Strength of Sheer Legs. 
Construction and Calculation of Stress on Members of a Steam 
Crane. Crane Shafts. Crane Chain. Crane Foundations. Con- 
crete Foundations. Cylinder Foundation. Pier-head Founda- 
tion Page 206 — 240 

CHAPTER XVI. 

STRENGTH OF RIVETED STRUCTURES — STEAM BOILERS, ETC. 

Strength of Boiler Plates. Of Joints in Plates. Rivets. Proportions 
of Joints. Oval Rivets. Double-cover Plates. Single and Double 
Riveting. Plates with thick Edges. Diagonal Joints. Strength of 
Boilers. Resistance to Collapse. Provision for Expansion and 
Contraction. Flues. Hydraulic Test. Strength of Cylindrical 
Boiler without Flues. Strength of Boiler with Flues. Tubular 
Boiler. Firebox Stays. Butt and Lap Joints. Welded Joints. 
Resistance of Tubes to collapse. Fairbairn's Experiments. Elliptical 
Tubes. Effect of Length on Resistance to internal Pressure. Small 
Tube Boilers 241 — 270 

CHAPTER XVII. 

ON STRUCTURES SUBJECT TO INTERNAL PRESSURE. 

Cast Iron Pipes. Pipes for High Pressures. Iron Tanks. Strengthen- 
ing by Wrought Iron Hoops. Thick Cylinders. Barlow's Theory. 
Gun Structures. American System of Casting Guns. Strength as 
depending on Exterior Form. Hydraulic Press Cylinders. Chilled 
Shot. Built-up Guns. Construction of Hoops. Armstrong's Sys- 
tem. Longitudinal Strain on Guns. Need of Mass in the Breech. 
Strengthening of Cast Iron Guns. Introduction of a Lining. General 
Conclusions • . . . 271 — 296 

Index 297 — 302 



PART I. 



ON THE STRENGTH OF MATERIALS EMPLOYED 
IN CONSTRUCTION, 



CHAPTER I. 

ON SOME OF THE PHYSICAL PROPERTIES OF MATERIALS. 

In order to understand that branch of applied mechanics 
which treats of the strength of materials, it is first of all 
necessary that the student should possess a precise know- 
ledge of those physical properties, on which the constructive 
value of a material and its adaptation for given circumstances 
depend. The fitness and reliability of materials for special 
purposes is by no means, exclusively, a question of strength, 
but is contingent on hardness, stiffness, toughness, mallea- 
bility, and other inherent properties, which result from the 
conditions of freedom or restraint existing amongst their 
constituent molecules. In judging of the suitability of a 
material for special duties, it is further necessary to know 
its powers of endurance under the action either of forces 
tending to abrade it, or of frequently repeated loading, or 
of vibration and impact, or of varied changes of tempera- 
ture, as the case may be. 

Our knowledge of the different kinds of materials now 
chiefly employed in connection with practical operations, 
has been extended by the publication of a large mass 
of valuable data, obtained in the numerous experimental 



2 On the Strength of Materials. 

investigations of scientific men, during the last hundred 
years, and particularly during the last quarter of a century ; 
more especially is this the case with the metals, cast iron, 
wrought iron, steel, copper, and brass. Hence, notwith- 
standing many discrepancies which occasionally present 
themselves, there are a great number of well ascertained 
facts and many definite laws for the guidance of those 
engaged in construction. 

To the young beginner, almost every kind of material 
with which he comes into contact appears to present a 
different appearance and character from that which it really 
possesses, or which it will appear to possess when he knows 
more about it. Thus, it may happen that a substance 
which, at first, seemed a hard, solid, rigid, continuous 
mass, is, in reality, soft and porous, and even movable 
in its internal structure; that every description of metal 
or wood is yielding and elastic ; that there is no such con- 
dition as absolute permanence of form, but that every mate- 
rial body suffers displacement of its parts under the appli- 
cation of external forces, being distorted or deformed, being 
extended, or compressed, or deflected, or twisted. The 
constituent molecules of some solids may even be made to 
slide over or amongst each other, may be spread out into 
a flat web, may be gathered into a more compact form, or 
may be crushed, to an extent dependent only on the strain- 
ing force which is applied. 

The apparent fixity and rigidity of solids is unreal, and 
this fact lies at the foundation of the whole subject ; hence 
one of the most remarkable features for the student to 
observe, at the outset, is the unfailing mobility of the in- 
ternal structure of materials on the application of sufficient 
stress. The naked eye may not be able to detect the move- 
ment, because our perceptions are not sufficiently acute to 
notice the minute change that takes place, but there is a 
change following every application of force. Hence, it is 
found necessary to resort to testing instruments of various 



On some of the Physical Properties of Materials. 3 

kinds, in order to apply great straining forces and to make 
the precise movements of the mass visible. For example, by 
the use of a testing machine, it is found that a bar of 
wrought iron, one square inch in section, will be elongated 
y^-g-oth part of its length by the weight of a single ton, and 
will continue to stretch with every additional ton, until 
rupture takes place ; or, to give another example of 
mobility, the change of temperature between the extremes 
of summer and winter is sufficient to expand, or contract, 
a wrought iron bar to the extent of ^ny-^th of its length. 

At the present time, there is practically no exact theory 
known which can be said to express the extension or 
contraction of various materials, nor even of different 
samples of the same kind of material, because the physical 
conditions of the several pieces are not exactly alike ; hard- 
ness or softness and other conditions, due to previous 
treatment of the constituents of the specimen, step in to 
modify the result. The present object is, to show to the 
student the practical aspect of the case, and to explain 
the properties of some common materials, as they are met 
with in the workshop ; but in the latter part of the book, 
when considering the principles which determine the form 
and arrangement to be given to structures, it will often 
become necessary to fix arbitrary rules, founded on the 
average result of numerous experiments, and in the ap- 
plication of which the judgment will have to be exercised. 

That property by which bodies tend to occupy a deter- 
minate bulk, or in the case of solid bodies a determinate 
bulk and figure, under given pressures and at a given tempe- 
rature, is termed their elasticity. By virtue of this property, 
they oppose a resistance to forces tending to change their 
volume or figure ; and, if they have been deformed by the 
application of such forces, they return more or less completely 
to their original bulk and figure when those forces cease to 
act. A body is said to be perfectly elastic, which returns 



4 On the Strength of Materials. 

exactly to its original bulk, or, if a solid, to its original 
bulk and figure, after such distortion or straining, when again 
placed in the same conditions of pressure and temperature 
as at first. A body which imperfectly returns to its original 
condition after straining is said to be imperfectly elastic. 
For all solid bodies, there are known limits to the amount 
of straining force which can be applied, without producing 
a definite and measurable change of figure or fierma?ient set. 
The limit of straining force which can be applied, without 
producing any measurable permanent set, is termed the limit 
of perfect elasticity or, more simply, the limit of elasticity 
for the given material under the given kind of straining 
force. For less straining forces the body is, for practical 
purposes, sensibly perfect in its elasticity. For greater 
straining forces it is sensibly imperfect in its elasticity. It is 
found by experiment that, up to the limit of elasticity, the 
displacements suffered by the molecules of the body are sen- 
sibly proportional to the stresses which cause them, so that 
a double displacement is caused by a double straining force ; 
a triple displacement by a triple straining force ; and so on. 

This property of elasticity is the more perplexing, because 
the deformations of solid bodies are so minute, and often 
so difficult to detect or to measure. Wrought iron is usually 
considered as one of the most elastic metals within certain ■ 
limits, still its elasticity is far from perfect, except with a very 
slight stress, and most probably it may yet be found to be 
imperfect, even with the smallest load. Nevertheless, for 
practical purposes, Hooke's law, which supposes all bodies 
to be elastic within certain limits, may be accepted as suffi- 
ciently near to the truth. 

The elasticity of materials, when considered as a prac- 
tical question and as affecting the "mechanical arts, is an 
important physical property. It is a property which is 
largely taken advantage of for most purposes, and for some 
other purposes it has to be carefully counteracted or guarded 
against. 



On some of the Physical Properties of Materials. 5 

The perfect elasticity of some solids within certain limits 
of straining force, is proved by this circumstance, that many 
such bodies suffer an innumerable number of repetitions of 
straining action, without being sensibly altered. A steel 
watchspring will work on for a century and give no marked 
symptom of change, and a twisted steel or even iron rod will 
shut a door for an unlimited number of times, and a chain 
or rod of iron will lift weights and submit to be lengthened 
and shortened constantly, for a long period, and apparently 
will recover its normal shape when the force is removed. 
But, most probably, this is so only because our means of 
observation are incapable of detecting the change which 
is gradually taking place. 

Those other materials, which do not exhibit this property 
to the same extent, or which readily retain any new form 
which may be imparted to them, are usually considered 
as non-elastic, and indeed justly, for practical purposes, 
although, strictly speaking, they are only very imperfectly 
elastic, as is evident when they are subjected to careful ex- 
periment : such materials are often termed plastic materials, 
as for instance, soft lead, putty, clay, and similar substances. 

Aeriform bodies, such as steam, air, and other gases, have 
no elasticity of figure, but are perfectly elastic as regards 
volume, for they may be expanded or compressed to an ex- 
traordinary extent, the expansion or contraction under con- 
stant temperature being sensibly proportional to the force 
employed to act upon them. 

A very common error exists respecting the elasticity of 
liquids, such as water : they are frequently treated as if they 
were without elasticity ;. but this is not strictly the case, ex- 
cept as regards elasticity of figure. Water does not seem to 
admit of being drawn out beyond the volume which is due 
to the pressure with which it is surrounded, and which in an 
open vessel is determined by the pressure of the atmosphere 
and its own depth. But when confined, water admits of a 
limited amount of compression, and when the pressure is 



6 Oji the Strength of Materials. 

removed, it instantly returns to its original volume, and so 
far is perfectly elastic. From the result of some careful ex- 
periments it was found that the pressure of one atmosphere 
reduced the bulk of water by nearly the 2-ooWo tn °f lts 
original volume, an amount so small as to be scarcely ap- 
preciable in practical operations, and which, as a rule, is dis- 
regarded. Even in the action of the hydrostatic press, work- 
ing often with a pressure of 500 atmospheres, it may be 
neglected with no practical disadvantage ; nor is the elas- 
ticity usually observable, in consequence of the greater 
movement of the surrounding metal interfering. 

It is due to the great compressibility of elastic gases, such 
as air, and the incompressibility of liquids such as water, 
that machinery for working with the former can be driven 
at a much higher velocity than similar machinery working 
with the latter. From the greater compressibility of air or 
steam, and the work absorbed in compression, there is not 
that perceptible shock which occurs with water or with 
solids under similar circumstances. It is this compressibility 
which imparts to aeriform fluids such a degree of yielding 
softness when they are acted upon by mechanical apparatus. 

The elasticity of solids is of a different character to that 
shown by gases or liquids, although many solids partake of the 
properties of the former in some degree. In solids, the elastic 
property is mostly shown in the more or less complete 
recovery of the original form, rather than in the recovery of 
volume, after compression or extension, and although within 
certain limits the elasticity of solids, such as the metals, 
may seem practically to be nearly perfect, still it is doubtful 
if they are entirely so. By very careful testing of long bars, 
it was found that they did not return to precisely the original 
length. This change is not easily observed in making 
experiments with short specimens, the alteration being so 
minute. 

Another notable feature is the circumstance that the 
stretching of a rod, or chain, or bolt, when subjected to ten- 



On some of the Physical Properties of Materials, 7 

sional strain, is not uniform unless the substance or strength 
of the bolt or chain is uniform. The greatest extension 
takes place at the weakest point, which is a great disad- 
vantage ; hence rods, bolts, or chains are frequently broken 
with less force, tear, and wear than would be inferred, if this 
fact were neglected. 

The elastic property of solid materials takes a much more 
important part, in the stability of structures, than is usually 
apparent to the casual observer. A familiarity with the test- 
ing machine and the lessons which it teaches, cannot fail to 
render the constant presence of elasticity a living reality to the 
thinking mind, and this should never be lost sight of, because 
any variation in the length of parts that have to support 
each other introduces an element of weakness. The long 
bolt, or the long stay, may not, on this account, take a fair 
share of the work ; and even in a single part, where the 
strain enters upon it by flanges, as»4n pillars, or by joints, as 
in tie-rods, unless we assume absolute perfection in the me- 
chanical fitting, some portion may have more than its share 
of duty ; hence it is that such end parts, so exposed, require 
to be made stronger than the main body. 

Notwithstanding this, the elastic property, which is so 
prominent a feature in all the materials which are employed 
in the workshop, is of inestimable value, as without it the 
iron could not be hammered or otherwise roughly manipu- 
lated. The great freedom of treatment to which the metals 
may be subjected, in reference to their malleable and other 
properties, is greatly due to their elasticity. 

When a rod of iron, or a beam, is in a normal or quies- 
cent condition, its capacity for rigid duty is not equal to 
that of a similar rod or beam in which the elasticity has 
been partially used up, by bending it into such a curve as will 
•not injure its future stability. 

By using up, or calling into active exercise, the elasticity 
of a beam or other article, the strength, or rather the stiff- 
ness, is considerably increased, and great ingenuity is fre- 



8 On the Strength of Materials. 

quently shown by practical men in such adaptations, whereby 
a comparatively flexible beam, by being subjected to a bending 
force, is thereby enabled to afford an amount of rigidity con- 
siderably greater than would be obtained from a much 
stronger beam, when left in its natural state. A beam fixed 
between the walls of a building, on which are to be erected 
the supporting columns of a steam-engine, will have a con- 
siderable amount of spring and vibration, unless the beam 
is inordinately strong ; but if this beam is firmly propped in 
the centre, and then bent down at the ends, by means of 
wedges within the wall boxes, the elasticity of the beam 
will be used up and the stiffness very greatly increased. 

Another example is afforded in the case of long horizon- 
tal tie-rods. The elasticity of the rod permits it to bend 
into a curve, due to gravitation. But by first ascertaining 
how far the rod will bend, and bending it previously to 
the same extent before it is erected, and then fixing it in a 
position in which the camber is upwards, the after-bending 
will bring the rod down to a straight line. The rod under 
such conditions is not only more pleasing to the eye, but is 
in all respects more rigid, from the elasticity being absorbed 
by the arrangement. 

In the familiar case of the springs of railway carriages, 
it is found advantageous to use up a considerable portion of 
their elasticity in the primary adjustment, by means of a 
rigid bar to which they are bound. By this means, the car- 
riage does not sink as the passengers enter, and the springs 
are so arranged that the remaining elasticity comes into play 
when the carriage is nearly full. 

It may appear inconsistent, to speak of a beam or rod 
being thus stronger by using up so much of its strength, but 
such is the case, for the class of purposes here indicated ; 
they are rendered stiffer with a given quantity of material, 
and it takes a greater stress to give further movement to the 
beam or rod. 

In the application of wrought iron, steel, and all the 



On some of the Physical Properties of Materials. 9 

highly elastic materials, although they may be safely loaded 
up to near their limit of elasticity, still, owing to the un- 
certainty of perfection of the material, engineers seldom 
venture far beyond the half of the amount of stress, which 
the apparent limit of elasticity appears to warrant. 



CHAPTER II. 

ON THE EXPERIMENTAL TESTING OF MATERIALS. 

Before describing the nature and manipulation of a mecha- 
nical testing apparatus, it is necessary to make a few pre- 
liminary remarks,- both in regard to the mode of carrying 
out experiments that are to be reliable, and to the care, 
precision, and accuracy which are required, and to draw 
attention to some of the many contingencies that may pre- 
vent the attainment of true results, or bias the mind of the 
operator, even where good instruments are employed, and 
with every desire to avoid error. 

In making important experiments with solid materials, it 
is not advisable, and can never be satisfactory, to depend 
upon the result of an experiment upon a single specimen, 
however good it may appear to be, for the smallest defect 
or scratch upon the outside, or even a hidden fault in the in- 
terior, may modify its behaviour to an unknown degree. The 
stress which is applied will mostly expend itself upon the 
specimen at its weakest point, instead of being distributed 
throughout the mass operated upon. Three specimens at 
least should be tested, and the diameter, length, and quality 
of each specimen should be uniform, as far as may be 
practicable. 

It is found, in the testing of short and long specimens, 
even of the same kind of material, that in general the short 
and long pieces do not all stretch alike, or in the proportion 
due to their respective lengths : the long bars stretch more 



10 On the Strength of Materials. 

than the short ones. The cause of this discrepancy is 
rather obscure, and it is doubtful whether it is owing to the 
long bar, from its mere length, having a greater propor- 
tionate risk of invisible defects, or to some other unknown 
cause ; but practically it is found that greater uniformity is 
attainable with short specimens, possibly in consequence 
of the closer scrutiny to which they may be subjected. 
Hence it may be inferred, that in testing materials intended 
for a particular structure, the nearer the test bars approxi- 
mate in their dimensions to that structure, the more reliable 
will be the average result for the particular duty. At the 
same time, the length does not affect the strength, for 
with the exception of weakness due to hidden defects, the 
actual ultimate tensile strength of any portion of a specimen 
is not much, if at all, affected by the length of the bar ; each 
portion has to act independently and for itself, irrespective 
of the other parts, its behaviour being exactly according to 
the stress to which it is exposed, and this is not inconsistent 
with the disproportionate rate of extension of long and short 
specimens, referred to previously. 

In testing bars or strips of metal, whether the pieces are 
long or short, but more especially in the latter case, it is of 
much importance that the stress should be applied to the 
specimen in a line coincident with the axis of the specimen; 
if it is not, the result will be erroneous, because, the stress 
not being uniformly distributed on the cross sections, one 
side will have to yield prematurely, and thus the resistance 
of the bar will be overcome in detail : for want of attention 
to this particular, many experiments made with rough appa- 
ratus do not afford reliable results. 

Time is an important element in the movement of the 
molecules of the specimen. In carrying out experiments 
with metals in a testing machine, it is evident that the 
period of time during which the specimen is exposed to the 
stress must, as a rule, be limited. With a short duration of 
time and a short specimen no ' permanent set' can be 



On the Experimental Testing of Materials, 1 1 

detected, if the load does not exceed a certain limit. To 
that special limit attention is directed, as it is a most im- 
portant one for the student to understand thoroughly ; it is 
usually termed the limit of elasticity, and is as varied for 
different materials as the point of ultimate rupture. But the 
fact that the testing machine does not show permanent set 
until the apparent limit of elasticity has been exceeded, 
does not prove much, for it is quite possible that a long con- 
tinued permanent load, or an often repeated application of 
a load not exceeding that limit, might ultimately fix the mole- 
cules in a new position ; on this point, however, a difference 
of opinion exists, though the experience derived from 
thousands of carefully performed experiments, with short 
specimens, in an accurate machine, would lead to the con- 
clusion, that within a certain range every metal returns to its 
original dimensions, as near as can be measured with mode- 
rately refined instruments. 

It is more than probable, however, that the first applica- 
tion of a load, much less than that commonly supposed to 
mark the limit of elasticity, does produce a minute perma- 
nent set. From the experiments made by the Commis- 
sioners appointed to enquire into the Application of Iron to 
Railway Structures, it would appear that with the smallest 
stress applied, namely, '56 ton per square inch, a minute, 
but perceptible, amount of permanent set was produced 
upon a 1 bar 50 feet long. When the stress was equal to 
1*69 ton, the set on the bar was equal to '0025 inch, 
or the *ooo, 004th of the length of the bar, an amount so 
exceedingly small that it could not be measured in speci- 
mens only a few inches in length. For practical purposes, 
the permanent set in such cases may be disregarded, being 
inappreciable. 

For the present purpose, it will be assumed that there is 
a limit of stress up to which every specimen is perfectly 
elastic, so far at least as our means of measurement permit 
us to ascertain. In making experiments on the value of 



12 On the S 'trength of Materials, 

different materials, one great object is to determine this 
limit of perfect elasticity. The operator must observe with 
extreme care the indication of the slightest permanent set, 
on the removal of the load. The limit of elasticity marks 
the maximum stress which can be exerted on a material 
without producing permanent deformation and therefore 
danger of ultimate rupture. But there still remains an 
amount of strength beyond the elastic limit, and which is a 
margin of safety in reserve. If a bar has been strained 
beyond the elastic limit and has taken a permanent set, it is, 
paradoxical as it may appear, in one sense stronger than it 
was before ; that is to say, it will require a greater strain to 
be applied, in order to move the molecules a still greater 
distance and to cause them to take an additional set. This 
is an important fact, and it is at once observable, when 
making experiments with short specimens, that no new load 
which may be applied, less than that which produced a 
given permanent set, will practically carry the effect farther 
onward. Therefore, by taking a permanent set, the limit of 
elasticity has in fact been raised, as the bar win not perma- 
nently stretch any more, without being subjected to a still 
greater strain. Even this, however, is not strictly correct, if 
the loads are much in excess of that which corresponds to 
the elastic limit. 

The elasticity of the several materials that are employed 
in the workshop is extremely unequal, both in degree and 
in the manner in which the condition is shown. For ex- 
ample, some solids have elasticity combined with hardness 
and brittleness in a high degree, and are similar in character 
to glass ; such are some kinds of cast iron, hard steel, and 
certain mixtures of copper and tin, in which, tested by 
impact, the elasticity seems as perfect as in an ivory ball, 
yet, in the testing machine, the extent of movement is so 
small that it can scarcely be measured by fine instruments, 
and for any practical purpose cannot be taken advantage of ; 
while, on the other hand, there are some of the metals that 



On the Experimental Testing of Materials. 1 3 

seem to have the properties of india-rubber, but in a less 
degree ; such is wrought iron, in a certain state, and still 
more so mild cast steel, when tempered in a particular man- 
ner, which developes the property of elastic flexibility in an 
extraordinary degree. 

In preparing various classes of specimens for the testing 
machine, the strength of the machine itself must be first 
taken into account, and this will determine the size of the 
specimens according to their strength. It is usual to have 
the several specimens carefully prepared in a lathe, of 
sizes nearly inversely as their strength, or in some propor- 
tion to their respective tenacity. It is extremely convenient, 
and it simplifies the subsequent calculation, to make them of 
such a diameter that their sectional area will be a convenient 
multiple or fraction of a square inch ; say, for instance, one 
square inch, half a square inch, or one quarter of a square 
inch. The Figures 1, 2, and 3, show the form and relative 

Fig. 1. 




14 On the Strength of Materials. 

sizes of such specimens of cast iron, wrought iron, and 
steel, as are commonly used in the testing machine now 
to be described, and which has been used in the Royal 
Arsenal at Woolwich, since 1854. The drawing is made to 
a scale of one -half of the usual size of the actual specimens, 
when prepared for the testing machine, and the peculiar 
shape which is given to these three specimens is that which 
is used for experiments on tensile resistance, the middle 
portion being the part which is to be tested, and which is 
carefully turned in a lathe, so as to be perfectly parallel 
throughout ; the ends of the specimens are enlarged as shown, 
in order to enable the machine to take a firm direct hold, 
and the advantage derived from the round form is chiefly 
this, that the specimens are produced in a lathe, with ex- 
treme accuracy, at a comparatively small cost for labour, 
and are in every respect as convenient and serviceable as if 
they were square, or of any other form. 

Specimens for ascertaining the resistance to a compres- 
sive stress are generally made in the form of short solid 
cylinders, of such dimensions as can be overcome by the 
power of the testing machine, and therefore are so simple 
in form that a further description of them is unnecessary. 

In the construction of the earlier mechanical testing ap- 
paratus, the mechanism generally consisted of a simple lever, 
which was mounted upon knife-edges at the several centres 
of motion and suspension, the short end of the lever 
laying hold of the specimen by a suitable bridle, and the 
weights being applied at the other end of the lever in the 
same manner as in a weighing beam. Great accuracy 
might be arrived at with such a simple lever, and some 
modern machines are fitted upon this principle and supplied 
with every requisite for testing the' strength of the weaker 
class of materials, such as bricks, stones, mortar, Portland 
cement, glue, the bite of nails in wood, or for similar 
purposes ; but they are not so convenient as those on the 
compound-lever arrangement, when great straining forces 
are required. 



On the Experimental Testing of Materials. 1 5 

In the modern construction of testing machines, intended 
to operate upon very large or very strong specimens of 
different kinds of metal, the lever arrangement is being 
superseded by some modification of the hydraulic press. 
The hydraulic press affords the most convenient means of 
giving the necessary strain, but in the older machines, the 
means of measuring the strain applied were imperfect. The 
best kind of hydraulic machines are so contrived that the 
precise force, which is exerted by the water, is shown by a 
delicately adjusted steel-yard, or some other modification of 
the lever principle. The lever is selected as more certain 
and reliable than pressure gauges, because, however carefully 
the latter may be constructed, they are liable to alteration 
and error. In addition, when the load has to be calculated 
from the pressure in the press cylinder, the friction of the 
ram must be allowed for, and this cannot be done with any- 
great accuracy. 



CHAPTER III. 

ON A MACHINE FOR TESTING THE STRENGTH AND 
ELASTICITY OF MATERIALS. 

The apparatus now to be described is intended to show the 
strength and elasticity of materials in various ways. It is 
probably one of the best and most correct machines which 
has yet been made, for the purpose of testing small short 
specimens, and for affording extreme accuracy in the results, 
so far as is possible with short specimens. The machine is 
shown in Figs. 4 and 5. This form of testing machine origi- 
nated in the United States of America ; the first one 
was brought to England from that country in 1854 by the 
author : since then many similar machines have been made, 
variously modified in size and arrangement, and have 



On the Strength of Materials. 




Ennmgnffigjjl 



(I *>\ 




Testing Machine. I J 

found their way to other countries. The machine in daily 
use at Woolwich, with which, during the last fifteen years, 
many thousand experiments have been made is also of 
this construction ; it is principally employed in testing 
specimens to ascertain their tensile and compressive resis- 
tances. 

The extensive application of machines on this principle is 
chiefly due to their simplicity and compactness of construc- 
tion, and the great convenience which their several arrange- 
ments afford for various classes of experiments, as well as 
their extreme accuracy. They are provided with suitable 
bridles, holders, and other apparatus, to test tensile, compres- 
sive, transverse, and torsional resistances, and are adapted 
for experiments on the force required to punch or shear, 
on the hardness or softness of bodies, and on the flow of 
solids. 

Figure 4 is a side and Fig. 5 an end elevation of this 
machine; the former shows most of the details, and will 
enable the general arrangements of the machine to be 
understood, with a little explanation. It consists of a 
combination of two levers, a and b, which together give 
a purchase of 200 to 1 ; that is to say, 1 lb. applied to the 
end of the upper lever at c will exert a stress of 200 lbs. 
on the specimen at s, and as all the bearing points of the 
entire lever apparatus are hard knife-edges, on hard smooth 
surfaces, the friction is reduced to a minimum. 

Where so much accuracy is aimed at, it will be neces- 
sary, before commencing an experiment, for the attendant to 
see that the machine is nicely balanced, not only in regard 
to its own members, but likewise with reference to the 
various appliances which may have to be employed in 
order to carry out the experiments, any of which may 
disturb the equilibrium. This adjustment of the balance is 
effected by the small weight d on the upper lever, which is 
used in the steel-yard fashion, until the machine is accurately 
adjusted ; if the want of balance is the other way, the adjust- 

c 



1 8 On the Strength of Materials. 

ment is made at the opposite end of the lever at e, by the 
suspension of as much weight as is requisite to secure 
perfect adjustment and to render the action of the machine 
as delicate as that of a weighing-machine beam. 

The testing weights used are, for convenience, of a pecu- 
liar form, to adapt them for being placed upon shelves on 
the small rod of iron, which is shown suspended from the 
end of the lever at c, each weight being accurately ad- 
justed, so as to exert a definite stress upon the specimen 
under operation. The plan of the weights is shown at w w ; 
they are round in form, with a slit extending from the out- 
side to the middle, to enable the operator to slip them easily 
into position upon the suspension rod. Several sizes of 
weights are used : the largest weighs 25 lbs., giving a 
strain of 5,000 lbs. on the specimen— of these there are 
nine ; of the second size there are ten, each weighing 5 lbs., 
or giving a strain of 1,000 lbs. on the specimen j of the 
third size there are also ten, each. weighing -|- lb., or giving 
a strain of 100 lbs. on the specimen ; thus making a total 
of 56,000 lbs., or 25 tons, which is the greatest stress that 
can be safely exerted by the machine. 

The operator is, by past experience, enabled to judge of 
the effect which will be produced on the specimen, by the 
respective weights as they are applied one after the other, 
and so is able to load the specimen gradually up to the 
required limit. As the critical point is being approached, 
he uses smaller sized weights, until they are equal in effect 
to a larger one ; he then removes the smaller weights and 
puts on a larger one as their equivalent, and continues 
with the smaller size, until their aggregate weight is again 
equal to that of a larger, and so on until the end is at- 
tained. When extreme accuracy is necessary, the utmost 
care has to be observed in the application of the weights, 
so as to avoid all rashness in the mode of carrying out the 
experiments. 

When a specimen is subjected to a strain, it immediately 



Testing Machine. 19 

commences to stretch, and as the leverage of the machine 
is 200 to 1, will the stretch be magnified in the same 
proportion ; that is to say, a stretch of xJ-o th of an inch in 
the specimen will cause the end of the lever to drop and 
the weights to sink 2 inches. Such a condition would be 
inconvenient, and therefore has to be provided for, and in 
this machine the effect of the stretching is compensated by 
the arrangements of the machine, which admits of adjust- 
ment at the point of suspension, the fulcrum of the upper 
lever being raised or lowered by means of a screw. As the 
specimen stretches, the fulcrum is proportionately raised, 
and this raising of the fulcrum is continued simultaneously 
with the stretching, and therefore the upper lever is con- 
stantly being raised and kept in a horizontal position during 
the operation. As it requires considerable power to mani- 
pulate the screw, a train of bevil- wheels and spur-gear is 
employed as an auxiliary ; this part is seen more clearly in 
the end elevation at g. When the screw is running down, 
or when the strain is not great, the spur-pinion is dispensed 
with, and a handle is slipped into the spur-wheel, then the 
pinion is thrown out of gear, and thus the operation of 
tracing the limit of elasticity is greatly facilitated, by the 
promptitude with which the change in position of the levers 
may be effected. 

If there were no provision for the jerk, with which the 
upper lever would necessarily go down, when final rupture 
takes place, it would be liable to be broken or bent at the 
termination of each experiment ; this is prevented by means 
of a sliding stopper h, which is made of wood and is con- 
structed with a slit or opening through which the end of the 
lever is passed, with just sufficient room to give the lever 
freedom to play, and in order to have this sliding board 
always in a proper position of readiness for the fall of the 
lever, this sliding stopper is moved up or down by the 
same screw movement which raises the fulcrum. Corre- 
sponding racks are placed at each end or side of the machine, 

c 2 



20 



On the Strength of Materials. 



with a horizontal spindle or shaft, geared at it ; hence the 
movements of both the fulcrum and board are simultaneous, 

Fig. 6. 




Fig. 7. 




Fig. 8. 




and the lever is caught by the wooden stop, before it has 
fallen a quarter of an inch. 

In the Figs. 4, 5, the testing machine is shown as it 
would be arranged for ascertaining the tensile properties of 
materials. By referring to Figs. 1, 2, 3, the form of specimen 
will be seen ; and in Fig. 6 is shown an enlarged view of the 
holder for tensile experiments. The ends of the specimen are 
held in carefully made split sockets, that fit the ends exactly, 
the two halves of the socket being kept together by rings 
or collars, which are slipped over and embrace them firmly 
without any effort or adjustment, and which may be easily 



Testing Machine. 2 1 

removed by simply tapping them with a wooden mallet. 
Thus the change from one specimen to another is made 
without difficulty. 

The machine being ready for an experiment, and the 
specimen in place, we may suppose that a weight is 
applied. If the specimen is of wrought iron, and is sub- 
jected to a stress of one ton per square inch, the middle 
or parallel portion of the specimen will perceptibly elon- 
gate, a distance equal to the l0 ^ 00 th part of its length, 
and the end of the upper lever will sink 200 times that 
amount. If a proper measuring gauge is pushed between 
the shoulders of the specimen and accurately applied, it 
will be shown that such is the case, and, so long as the stress 
is continued, it will remain thus stretched ; but if the strain 
is now removed, it will in time return again to the original 
length, thus showing that the material is so far elastic. On 
reapplying the stress, it will again stretch, and with every 
addition of one ton it will take an increment of extension 
in about the same proportion, and again and again return, 
if the weights are removed, nearly to its original place. 
This will continue up to a certain limit of load, of about 
10 tons per square inch for wrought iron ; under that point 
the specimen will return almost to its former dimensions, 
but beyond it the return will not be nearly so perfect. 

It has to be explained, however, that the statement in the 
preceding paragraph, that each ton of stress applied to a 
square inch of wrought iron will cause an elongation of 
T O o 00 th of the length, is only approximately correct. This 
amount of elongation is rather over than under the usual 
amount of extension ; but it is so near that, for all practical 
purposes, it may be accepted as correct. For each addi- 
tional ton of strain, the bar will stretch another 10 ^ 00 th, 
until the limit of elasticity is reached, which as a rule is found 
between 8 and 1 2 tons, according to the quality of the wrought 
iron tested. Hence, 10 tons is usually considered to be the 
average limit of elasticity of moderately good wrought iron, 



22 On the Strength of Materials. 

and the total stretch, up to that point and with that load, 
amounts to very nearly yoVo^ °f tne length of the part ope- 
rated upon. It is nevertheless very difficult to ascertain the 
true limit of elasticity, and published results often show great 
discrepancies as to the limit at which permanent set was 
first observed. In such cases, a judgment must be formed 
as to the value of the results, which depends on the accuracy 
of the testing machine employed, and the care and skill 
of the experimenter. 

Some very careful experiments were carried out by the 
Commissioners, who were appointed to enquire into the 
Application of Iron to Railway Structures, with especial 
reference to this point, and the results are embodied in 
a Table at page 58. If such a course of experiments were 
repeated a few hundred times, so as to confirm the result, 
the natural law might probably be inferred, and, as will be 
seen by a reference to the facts in the Table, the minute 
results therein shown are consistent with the more general or 
approximate data given above. Still, that valuable Table only 
serves for the one or two specimen bars which were ex- 
perimented upon ; and those who have made many experi- 
ments are always impressed with the extreme variation of 
almost all the properties of materials, in different specimens, 
and especially of the limit of elasticity and the point where 
permanent set commences. In some specimens which were 
cut transversely from a large mass, the elastic limit was 
found to be under four tons of strain per square inch, while 
in other specimens of the same iron, but in the form of good 
rolled bar, of smaller sizes, it was found to have risen to 
about 1 2 tons per square inch, and generally that particular 
iron had a limit of elasticity ranging from 8 to 12 tons. 

When the elastic limit is reached by the operator, then the 
future behaviour of the bar under trial will altogether depend 
on the precise nature of the iron. If it is soft and ductile, 
the iron will be drawn out to a much smaller diameter in 
the neighbourhood of the point of fracture, before the final 



Testing Machine. 23 

rupture takes place. Although under such conditions it is 
usual to consider the breaking load as so much per square 
inch, calculated from the original dimensions, still, in point of 
fact, the ultimate strength is really more than that; because, 
from the altered diameter of the specimen at the moment of 
fracture, its area may have been reduced to fths of the original 
area. This peculiarity is sometimes termed toughness ; such 
iron will aiford good warning before breaking, and is conse- 
quently preferred for purposes where repeated tension has to 
be exerted. 

During the performance of the foregoing class of experi- 
ments, the operator has to watch carefully the behaviour of 
the specimen, in order to note its general character, for by 
continuing to increase the weight, gradually, upon the end of 
the lever, the whole of the characteristics of the specimen 
develope themselves, more or less clearly, and the appear- 
ances observed will much depend on its own inner nature. 
In some, the metal will flow, or be drawn in the heart of the 
bar only, thus leaving a corrugated exterior surface from the 
crumpling of the outer skin; in other specimens the flow 
is more uniform, and the outside is comparatively smooth. 
If, on the other hand, it is hard and rigid, it may not be 
drawn out to any great extent, but may break, with very little 
reduction of sectional area, and exhibit a high tenacity. If, 
on the contrary, it is of a soft and fluent nature, it will flow 
freely and be drawn out to a considerably smaller section, 
and then will break at the point where the diameter is most 
reduced. It may even now give a total strength varying 
from 20 to 25 tons per square inch of the original dimen- 
sions. The testing machine is equally suited for any other 
kind of metal ; and, in dealing with familiar materials, such 
as cast iron, steel, copper, bronze, or other alloys, in order 
to arrive at their tensile properties, the same course is pur- 
sued as with wrought iron. 

In arranging the machine to test compressive resistances, 
the shackles which hold the specimens for tenacity are re- 



24 On the Strength of Materials. 

moved, and another description of instrument is put in the 
same position in the machine. This instrument is shown 
in Fig. 7. It consists of two parts, a and b, the one 
sliding within the other, one of the parts being attached 
to the "lever, and the other part to the framing of the 
machine. The specimen for this purpose is in the form of a 
small cylinder • weights are applied to the end of the upper 
lever, producing a stress 200 times as great on the speci- 
men, in consequence of the leverage, which is the agency 
employed in compression. As movement takes place, either 
from the elasticity or the permanent set of the material, 
the fulcrum of the lever has to be moved, so as to keep 
the proper position ; this is accomplished by turning the 
handle, which gives motion to the vertical screw, shown 
at g in Fig. 4. 

A specimen-holder, nearly similar to that used for com- 
pression, is likewise used for other purposes, such as 
punching, shearing, or indenting, and for testing the hard- 
ness or softness of materials. Such a specimen-holder is 
shown at Fig. 8. It is here arranged for testing the force 
required to produce a certain amount of indentation, and is 
applied to the machine in the same manner as the specimen 
holder for compression. 

In Fig. 4, in the side elevation of the testing machine, 
are shown a row of points marked k, k, k, k, k — these are 
knife-edges firmly secured, and are used in testing trans- 
verse resistances. In Fig. 9 is exhibited one of the usual 
anangements of the apparatus, when employed to test 
me transverse strength of materials. The bar, or rod, 
or small girder, is held up against two knife-edges, k^ k, 
and the load is applied at the centre ; the points of support 
are some definite distance apart, which is easily measured 
in this case. The distance shown is 10 inches ; but by 
looking to the points k in the machine, it will be seen that 
provision is made for increasing the distance to 20 inches 
or 30 inches. The bar is kept up to these knife-edges by 



Testing Machine. 



25 



the knife-edge contained in the holder at /, which is so 
constructed as to embrace the bar, freely, during the ex- 
periment. In this instance, as in all other cases, the weights 

Fig. 9. 




are applied gradually to the end of the lever ; at the same 
time the behaviour of the specimen is observed, in regard to 
its strength, elasticity, buckling, set, &c. Experiment shows 
that the strength of rectangular bars, supported at the ends 
and loaded at the centre, is inversely as the distance between 
the supports, and directly as the width or thickness of the 
specimen, and as the square of the depth. The width of the 
specimen is that dimension which is perpendicular to the 
plane of flexure, and the depth is the dimension in that plane. 
When a specimen is loaded transversely, it immediately 



26 On the Strength of Materials. 

commences to bend in a curve, which, in the case of 
wrought iron or soft steel, from the change of form in the 
cross section, indicates considerable movement to have 
taken place, amongst the molecules composing the part 
mostaffected. The respective parts of the bar under tension 
and compression seem to meet, or run into each other, 
but not in a line that would be indicated by a previous 
knowledge of the tenacity or compressibility j this is an 
element that should be taken into account in any calcu- 
lation of the strength of structures, when built up of the 
flowing metals. 

Again, looking to Figs. 4 and 5, at the point m, there is 
shown the end of a specimen which is secured to the frame 
of the machine by means of two cotters ; and the object of 
this arrangement is to ascertain the resistance of the speci- 
men to torsion, or to a twisting strain, like that which is 
developed in the case of a shaft employed for conveying 
motive power. Any form of bar may be secured by the 
cotters. The bar is fixed securely at one end, or it may be 
at both ends, but by having a vacant space between the fix- 
ings, sufficient room is left for a lever to be firmly secured in 
the middle of the specimen. The position of this torsion 
lever is shown at n ; and, as will be seen, the lever termi- 
nates with the outer end formed into a segment of a circle of 
some considerable range. To the lowest point of the seg- 
ment, there is fixed a suitable pitch-chain, which is carried 
round the segment and upwards, to be hooked on to the 
lower end of the suspension rod r, by which it is connected 
with the lever a, in the same manner as for tension and com- 
pression. 

It will be observed that the balance of the levers may 
be a good deal disturbed by this apparatus ; the machine 
has therefore to be adjusted by the weights d or e, after 
which the testing may be proceeded with. 

The point most necessary to be determined is the limit of 
torsional elasticity, which will be referred to in the Chapter 



Testing Machine. 27 

relating to Torsion. Experiments with bars of different sizes 
show that the torsional strengths of shafts of different sizes 
are to each other nearly as the cubes of their diameters, 
any departure from that ratio being probably due to some 
accidental cause. 

In making experiments, it is instructive to observe the 
deformation of ductile materials such as wrought iron and 
the softer steels, and to consider the action of the mole- 
cules composing the specimen, both when under tension 
and compression. The change of form which is observed 
can only be readily understood, by considering the metal as 
a fluid, the iron behaving in a manner similar to that of 
water passing through a tube or channel of any form. When 
a bar is drawn out, the principal flow of the, apparently, solid 
metal, is in the middle of the stream • and hence the peculiar 
sectional form which is assumed either by a round or 
square bar, or one of any other shape, showing that the 
farther the molecules of the material are removed from the 
centre of the flowing current, so much the less are they 
affected by the influence of the general movement. This 
unequal flowing of the molecules, may partly account for 
the apparent weakness of thin plates as compared with 
round bars of the same sectional area. 

With a flowing, malleable, or ductile metal, the round 
bar when under tension is drawn out to a small diame- 
ter, uniformly, all round, but the metal goes in the middle 
chiefly, and the outside is shrivelled ; while, with a rectan- 
gular or square bar, the flat surfaces are slightly hollowed, 
to an extent proportionate to their distances from the centre 
of the flow. Thus the corners become more prominent than 
they previously were. When cast iron is treated in the 
same manner there is no perceptible change of form, 
volume, or specific gravity, whereas with the flowing 
metals both volume and speciiic gravity are altered, the 
volume being increased and the specific gravity diminished. 
The strength is in some small measure interfered with by 



28 On the Strength of Materials. 

changes of form to which the material has been subjected 
during its manufacture. Good fibrous wrought iron is gene- 
rally a little stronger in the direction of the fibre than trans- 
versely to the fibre, but the difference in any case is very small, 
and the strength is commonly assumed to be practically 
the same in both directions. The behaviour of a piece of 
iron, in this respect, is quite different to that of a piece of 
wood, which is much stronger in the direction of the fibre 
than it is when fractured across the grain, or in any other 
direction. A bar of wrought iron when it leaves the rolls 
is in a condition of great restraint ; the exterior is not in 
perfect equilibrium with the interior of the bar, which at 
the commencement of an experiment affects the elongation 
and permanent set. The first effect of the application of a 
load is to liberate the constrained surface, and true condi- 
tions on which to form an opinion do not exist until equi- 
librium is established in the bar itself. Previous to that 
the result is deceptive; hence the advantage of carefully 
turned specimens. 

The structure of a rope or a bundle of fine wires does 
not accurately represent the condition of materials, such as 
wrought iron, or even wood. It will lead to a false conclu- 
sion, if we reason on the assumption that, in materials like 
wrought iron, the fibres of which it appears to be composed 
are detached and independent of each other, or that they 
slide with freedom as in a rope or bundle of wires. On 
the contrary, they are firmly joined together, side by side, 
with a force nearly, if not altogether, equal to their general 
tenacity. The idea of a flowing stream, in which the velo- 
city of the different parts depends on the stress applied and 
on their mutual adhesion and friction, represents much more 
truly the condition of a ductile bar Under strain. 

It is very interesting and instinctive to take a square 
bar of iron, the larger the better, and carefully bend 
it round a large mandrel, into a circle, and then to observe 
the alteration of sectional form which ensues, the thinning 



Testing Machine. 29 

away of the outer side and the increase of thickness at the 
interior, and the curved lines that gradually form and shade 
away from the one side or corner to the other. We can 
scarcely realise the changes that have taken place in the 
interior of such a bar, but they are strange and wonderful, 
and instructively illustrate many of the foregoing remarks, 
on the behaviour of a malleable, ductile, or flowing metal. 

The testing machine here described may appear compli- 
cated, but it is really a simple machine ; any appearance of 
complication arises from the smallness of the diagram, or an 
imperfect appreciation of its mechanism and manipulation. 
It is easily used, little besides care and patience is required 
to arrive at accurate results. 

By means of the various contrivances shown in the 
diagrams, combined with other expedients, almost any of 
the physical properties of materials may be ascertained 
by the testing machine, with sufficient accuracy for the 
guidance of those who have to apply them in the operations 
of daily life. Next to an acquaintance with the natural 
laws of mechanics, and to being familiar with the contri- 
vances that have been devised by men in all ages, for turn- 
ing the natural laws to account, a clear perception of the 
several properties of the materials that are to be employed 
in construction will be found most useful, indeed the value 
of such knowledge can scarcely be over-estimated. 



30 On the Strength of Materials. 



CHAPTER IV. 

CAST IRON. 

The usefulness of the different materials by which we are 
surrounded, measured by the extent of their application in 
the mechanical arts, has varied greatly in course of time. 
In past ages wood occupied a much more prominent posi- 
tion as a material of construction than it does now, having 
been superseded by metal for many of those purposes for 
which it was, formerly, exclusively employed. This substitu- 
tion of metal for wood would even have been still more 
complete, if the former possessed some of the peculiar pro- 
perties which render the latter extremely valuable for certain 
purposes. Amongst the metals, iron — either as cast iron, 
wrought iron, or steel — occupies now the foremost place 
among the materials at the disposal of the engineer. It 
is not strange, therefore, that, from their great importance 
in the arts, iron and steel should have been the subject 
of more experimental research than has been bestowed upon 
any other material. At the same time our knowledge is 
far from perfect, for there yet remain many obscure points, 
of great importance, which require further and frequently 
repeated investigation. 

Cast iron is the crude metal derived from the smelting 
furnace. The ore and fuel are thrown into the furnace 
together, an intense heat is generated by means of a strong 
blast of air, the refractory ore is thereby reduced, and the 
iron gradually melts and runs down to the bottom by gravity. 

Iron ore is very refractory, and in, general is found mixed 
with earthy materials. Hence, it cannot be reduced by the 
carbon of the fuel alone, but requires the addition of fluxes, 
capable of combining with the earthy materials of the ore 
and of facilitating their fusion. If the ore is argillaceous, 
or contains clay, then the flux employed has to be of a 



Cast Iron. 3 1 

calcareous nature ; whereas, if the ore is calcareous then 
clay is required as a flux, or, what comes to the same thing, 
the two sorts of ore may be mixed in suitable proportions, 
so that the one acts as a flux to the other. When the flux 
or third material is required, it is thrown into the furnace 
along with the ore and fuel, and at a high temperature it 
unites with the earthy matter of the ore and becomes slag, 
setting the greater part of the iron free. 

It will thus be seen that, at the very threshold of the iron 
manufacture, there are several causes in operation which 
may seriously affect the quality, as well as the cost, of the iron 
produced. The liquid iron having to be in such intimate 
contact with the fuel and flux and their impurities, its 
quality is necessarily exposed to danger and may be mate- 
rially affected by contamination with sulphur, phosphorus, 
or other injurious substances, present along with it in the 
smelting furnace. 

During this preliminary smelting process, the cast or liquid 
iron has ample opportunity of combining with and absorb- 
ing a considerable quantity of carbon ; this absorption of 
carbon in cast iron, whether in combination with the iron 
or not, is its distinguishing feature and determines its be- 
haviour in most respects. It is the presence of carbon 
which gives to it its fusibility and enables it to be remelted 
again and again, and thus renders it suitable for the founder, 
the degree of fusibility depending on the quantity of carbon 
which it contains. 

The presence of carbon renders the iron more liquid 
when in the fluid state, and softer and tougher when in 
the solid state. Still, when the iron has an excess of 
carbon, it is not so strong as iron with a less proportion 
of carbon ; hence the practical knowledge and judgment of 
the founder requires to be exercised, in the employment of 
the different sorts and in mixing those of different qualities, 
in order to obtain a metal with the requisite hardness, soft- 
ness, closeness of grain, strength, and toughness, for the dif- 
ferent kinds of castings which he has to produce. 



32 On the Strength of Materials. 

When iron contains carbon in great excess, a portion of 
it may be in an uncombined condition, and this influences the 
quality in the direction of fluidity, softness, and weakness. 
The proportion of carbon in cast iron varies from 5 per cent, 
to 2 per cent. Cast iron may be poured into moulds of any 
form, and when carefully treated has considerable tenacity 
and even toughness and compressibility. But at the best it 
is comparatively an uncertain metal, and gives little, or, 
indeed, no warning previous to ultimate fracture, which is a 
radical defect. 

In the preparation of cast-iron guns, where great strains 
are to be resisted, the conditions to be aimed at are rather 
contradictory. It might be inferred that the strongest sorts 
of iron would be the best for this purpose ; but guns made 
of such iron fail at proof from their brittleness, and a softer 
mixture stands the proof much better. On the other hand, 
the interior surface of the bore when made of soft iron is 
not sufficiently close in the grain. The opposite conditions 
thus indicated to be desirable, can only be obtained by a 
compromise, the iron used being hard enough not to be 
spongy, and soft enough not to be brittle. 

The best results, both in regard to elasticity and strength, 
are obtained by mixing a number of different kinds of cast 
iron, all carefully selected. Such a combination gives a 
higher result at the testing machine than the average of the 
different samples, when cast separately, yet the strength of 
the mass has seldom an ultimate tenacity exceeding 9 tons 
per square inch, and much oftener it is found nearer to 8 
tons. Sometimes the tenacity reaches 14 tons, and cast iron 
has been produced with a tensile resistance of 15 tons, but 
such a tenacity is rarely attained. The average ultimate 
tenacity of ordinary cast iron is about 7 tons, and in inferior 
qualities only 5 tons, or even less, but these are exceptional 
qualities, and are of no value for purposes where strength 
is of consequence. The quality used for guns should have a 
tenacity not less than 10 tons per square inch. 

In submitting cast iron to the testing machine, its limit of 



Cast Iron. 33 

elasticity, as shown by short specimens of common quality, 
is found to be rather low, or about one-third of its ultimate 
tenacity, but rather over than under; hence, in works of 
construction, it is not considered safe to strain ordinary cast 
iron, in tension, above 2 tons to the square inch, and even 
with the higher qualities, the greatest working tensile stress 
should never exceed 3 tons. For structures exposed to im- 
pact, the limiting stress should be much less, say 1 ton. It 
must be clearly understood, however, that these figures are 
only approximate. The student should closely study the 
Tables given at page 39, containing experiments on cast- 
iron bars of 10 feet in length, from w T hich it would appear that 
the limit of elasticity is much less than we have assumed 
above, being under -^th of the ultimate strength, and in 
which a permanent set was produced with a stress of j of a 
ton ; probably it would have been detected earlier, if the rod 
had been 100 feet instead of 10 feet long. Still, for practical 
purposes, it would be inconvenient to be governed by 
such minutiae of measurement, and the approximate figures 
given in Table I. are sufficiently accurate for common pur- 
poses. 

The following Table gives the extensions and elasticity of 
good cast iron, when the ultimate strength is about 10 tons 
per square inch of sectional area, which is considerably above 
the average for cast iron of commerce ; as before stated, it 
may be considered as the lowest quality admissible for guns. 

The first column shows the weights applied in lbs. ; the 
second column gives the load on the bar per square inch of 
its section, in tons ; the third column gives the visible mea- 
surable stretching while the stress is acting, within one 
minute of the application of the last increment of load ; the 
fourth column gives the permanent set when the weight is 
removed, or shortly afterwards ; the fifth column shows what 
may be considered to be the average elastic extension of a 
good specimen of cast iron. 

By looking down the columns it will be seen that the 

D 



34 



On the Strength of Materials. 



elasticity is apparently perfect with 4 tons, but that with 
5*2 tons there is a perceptible permanent set, equal to 
the quarter of a thousandth part of an inch, and although 
the elasticity continues to the end of the experiment, still 
the limit of perfect elasticity has been reached at some un- 
known point between 4 and 5 tons, or well up to half the 
ultimate strength, which is higher in proportion than with 
the common cast iron of commerce. 

Table showing the properties of cast iron, of the lowest 
quality suitable for guns : — 



TABLE I. 



Weight 


Stress in tons 


Visible stretch 
under the stress 


Permanent set 


Difference 
between the 3rd 


applied in 


per square inch 


at end of half 


when the load 


and 4th columns, 


lbs. 


of section. 


minute. 


was removed. 


showing the elas- 
tic extension. 


4OOO 


2 


•OOO5 





•OOO5 


600O 


3-0 


•OOI 


— 


•001 


7000 


3'5 


•OOI5 


— 


•OOI5 


80OO 


4-0 


•002 


— 


•002 1 


IO4OO 


5 "o 


•OO25 


•OOO25 


•OO225 


1 1600 


5-8 


•OO3 


•OO05 


•OO25 


I2500 


6-25 


•OO35 


•OO75 


•OO275 


I4OOO 


70 


•OO4 


•001 


•OO3 


I480O 


7'4 


•OO45 


•OOI25 


•OO325 


160OO 


80 


•0055 


•OOI75 


•OO375 


I7IOO 


8-55 


•OO7 


•OO25 


•OO45 


179OO 


8-95 


•OOS 


•OO3 


•005 


I8800 


9 '4 


•OI 


•OO45 


•0055 


1960O 


9-8 


— 


•OI55 


— 


20500 


10-25 


— 


•OI4 


Broke 



From the circumstance that the ultimate tenacity or ten- 
sile strength of castings of cast iron may vary between 1 5 tons 
and 5 tons per square inch of section, much attention has 
been given to the subject, both on the part of makers and 
of purchasers of castings, in order to secure qualities suit- 
able for particular duties — more especially has this been 
the case where strength alone was the chief consideration. 
It may be said that, for the majority of ornamental castings, 



Cast Iron. 3 5 

strength is of less importance, as for them the chief consider- 
ation is that the metal employed shall be extremely fluid, 
so as to enable it to flow like water, and fill up every rami- 
fication of the mould. In a less degree, the makers of the 
great majority of castings, for lathes or machine tools, aim 
rather at securing closeness of structure with a moderate 
degree of hardness than great strength, because mass for 
its own sake is of value in such articles, and this involves 
the presence of a quantity of material which renders the use 
of strong cast iron of less importance. 

For beams and girders, strength and rigidity are the first 
considerations. Some founders, who are very careful in 
regard to the strength and practical goodness of their cast 
iron for such purposes, go to the trouble and expense of first 
melting the several sorts of iron, collected to form the in- 
tended mixture, and running the mixture into pigs. These 
are afterwards broken into fragments, which are examined 
one by one and carefully selected ; those pieces which pre- 
sent the best fracture are laid aside for important castings, 
the other pieces being kept for castings of less importance. 
It is also usual, with such careful founders, to cast test bars, 
in order to ascertain, in a rough and ready manner, the 
approximate strength of the metal they use for their own 
guidance. 

A common method is to cast in a dry mould a bar 1 inch 
square by 54 inches in length, which is laid upon supports 
48 inches apart, and weights are suspended in the middle 
until it deflects f of an inch. Some sorts of cast iron are 
found too rigid to deflect much \ but good tough iron will do 
so invariably, and return again apparently uninjured. From 
hundreds of experiments made as above, it was found that a 
good mixture, properly cast, will sustain a load of 620 lbs. 
with a deflection of half an inch, while some have gone down 
the same distance with 240 lbs. Founders have ascertained 
that some sorts of cast iron, which are comparatively weak 
by themselves, will have their strength greatly increased by 

d 2 



36 On the Strength of Materials. 

being mixed with another sort of iron. Haematite iron, 
for example, sustained, as above arranged, 480 lbs. ; yet, 
when mixed with some Welsh iron, not of a stronger 
character, it carried a load of above 500 lbs. ; thus showing 
that the question of mixtures of cast iron is an important 
subject in itself, which opens a wide field for the scientific 
founder. 

Other founders, who contract for castings, are less careful, 
and have to be checked; hence, some engineers in their 
contracts for castings insist upon specimen bars being cast 
and tested, both for deflection and tensile strength. Such 
bars, of a section 2 inches by 1 inch, with a distance of 3 feet 
between the supports, are required to sustain a load, in the 
middle, of 30 cwts., and to deflect, before fracture takes 
place, at least '29 of an inch. A bar 1 inch square is 
required to sustain a tensile stress of nitons per square 
inch, which is a very high tenacity. Such a course is highly 
to be commended, and helps to stem the downward course 
to the cheap and worthless ; the student will do well to 
note the above, and he will find that, in the long run, it is the 
course which will best answer his purpose — weak and cheap 
material may do for a time, but its employment invariably 
brings its own punishment. 

It will be evident, that the mere casting of test bars does 
not afford absolute security that the castings shall be of the 
same quality. Some engineers, contracting for a large num- 
ber of beams or girders, on which the stability of an im- 
portant structure has to depend, have experienced consider- 
able difficulty in obtaining definite security that the proper 
quality of iron has been employed by the founder. In the 
case of cast-iron beams of the usual form, namely, with a 
vertical rib, and having the upper and lower flange in the 
proper inverse proportion to the tensile and compressive 
strength of the iron, they bend each girder separately by 
hydraulic pressure until they severally deflect the ^o-th part 
of their length. The pressure applied, as shown by the water 



Cast Iron. 37 

gauge, is said to be about the half of the force required to 
break them ; such a ratio, however, must depend on many 
conditions. A safer course, which is resorted to by some, 
is to cast an extra beam to every score that are required, 
or some other proportionate number, and then to test such 
a proportion of the beams cast, selected at random from the 
whole number, until actual rupture ensues ; if the test beams 
break under a given load, the whole number are rejected. 

Tables II. and III. refer to cast iron, and are compiled 
from valuable experiments made by the Commissioners 
appointed to enquire into the Application of Iron to Rail- 
way Structures. The first Table has reference to the be- 
haviour of the bars under tension, and the second Table 
to their behaviour under compression, the bars being 1 inch 
square and 10 feet long. 

From the length of these bars, and from the care bestowed 
upon the experiments, certain important data are furnished 
by them, especially in regard to the elongation and compres- 
sion, and the accompanying permanent set, with loads for 
which they are inappreciable in short specimens. The Tables 
would have been still more perfect, if the temperature had 
been noted. 

The actual measure of the permanent stability of any 
material is the point at which permanent elongation com- 
mences, and that point should have the chief attention. 
Still, if we are to trust these experiments, some judgment 
will be required, because, as Table No. II. shows, this point 
of commencing permanent set was only equal to i-ioth of the 
ultimate stress required to produce fracture, it is therefore 
necessary to take into account the ultimate strength as well, 
in order to know the margin of strength that lies beyond 
the elastic limits. With short cast specimens, this elastic 
limit, if in any degree observable, would appear to stand 
at a much higher point than that shown by these experi- 
ments, and, as before stated, it is usually considered to lie 
between the third and the half of the ultimate strength. 



38 On the Strength of Materials. 

As this Table shows, the iron is in some measure elastic 
even to the end, and yet can scarcely be said to be perfectly 
elastic even at the beginning of the experiment. Only a 
few experiments were made with long bars. If a similar 
course could be gone through with every description of cast 
iron — hard, soft, weak, and strong, in all their varieties — engi- 
neers would then be furnished with more clearly defined 
knowledge on these points than exists at present. Such an 
enquiry should be made, with special regard to the relative, 
fitness of different sorts of cast iron for different purposes. 
Precise data thus obtained would be of great advantage to 
practical men. 

From several hundred experiments made at Woolwich 
with selected specimens of the higher qualities of cast iron, 
the ultimate tenacity was found to range from 10,866 lbs. 
up to 31,480 lbs., the average tenacity being 21,173 lbs. P er 
square inch. This average result, although high, is under 
10 tons, and lower than the average of 850 samples, sent 
in for competition, the tenacity of which ranged from 
9,417 lbs. up to 34,279 lbs. per square inch. 

It will be observed that the best of these specimens 
had a tenacity over 15 tons, and the worst a little over 
4 tons per square inch. Similar experiments, carried out 
on a number of specimens of the ordinary cast irons of 
commerce, gave an average of 12,912 lbs., or a little over 
6 tons, and some specimens of Nova Scotia iron gave an 
average of 15,821 lbs., or a little over 7 tons per square 
inch. The foregoing were the ultimate breaking strains, 
and the specimens were only 2 inches in length. They 
gave no warning of fracture, that was perceptible to the 
senses with ordinary instruments ; but no doubt there was 
movement, if it could have been measured by suitable means, 
with verniers, for instance, that would read to the ioo,oooth 
part of an inch. 

Table No. II. shows the elongations and amount of 
permanent set with a given load of cast-iron bars one 
inch square and 10 feet long; these bars are of the same 



Cast Iron. 



39 



size as the wrought-iron bars of Table VII. A comparison 
of these Tables will show a great difference, irrespective of 
strength, between the behaviour of the cast and the wrought 
iron j the relation of weight to extension is not nearly so 
uniform in the cast iron. 

Table No. II. also shows that a permanent set took place 
with a load of 7 of a ton, or less than -jL-th of the breaking 
stress, which is not in accordance with the general notion ; 
the set, however, is so small that it could not be measured 
in a short specimen. The sixth column is the most in- 
structive, it shows the relation of weight to extension, which 
h far from being constant. 

Synopsis of experiments on the extension of bars of cast 
iron, 1 inch square and 10 feet long : — 



TABLE II. 







Extensions in 






Weights in 




Sets in 
fractions of 
of an inch. 


Ratio of 
weight to 
extension 

IV 


Fractions (Fractional 
of an inch ?**? of 






lbs. =w 


tons. 


1 entire 
length. 




e 


105377 


'47 


•OO9O 


1 

13333 


set not visible. 


I I 7086 


1580-65 


•70 


•OI37 


1 

8759 


•0OO22 


H5I3I 


2107-54 


*94 


•Ol86 


1 
6451 


•OOO545 


I I 3309 


3161-31 


I-4I 


•O287 


1 
4181 


•OOI07 


IIOI50 


4215-08 


i-88 


•O39I 


1 
3069 


•OOI75 


IO7803 


526885 


2'35 


•0500 


1 
2400 


•OO265 


105377 


6322-62 


2-82 


•0613 


1 
1957 


•OO372 


I03 142 


737639 


3-29 


•0734 


1 

1634 


•005 1 7 


IOO496 


8430-16 


376 


•0859 


1 
1396 


•00664 


98139 


9483'94 


4-23 


•0995 


1 
1206 


•00844 


95316 


IOS377I 


47o 


•1136 


1 
1056 


■OIO62 


92762 


11591-48 


5'i7 


•I283 


1 
903 


•OI306 


90347 


12646-25 


5-64 


•I448 


1 

828 


•01609 


87329 


13699-83 


6-u 


•1668 


1 
1 7T9 

645 


•02097 


82133 


I4793-IO 


6-6o 


•1859 


•O24IO 


79576 


16664-00 


7-43 


mean break- 
ing weight. 1 








Api 


>arent Lin 


lit of elasticity, i of b 


reaking \vei£ 


Jht. 



Although the property of tenacity is that which receives 



40 On the Strength of Materials. 

the greatest attention, for many practical purposes the 
resistance which is offered to compression is also of great 
importance. 

Cast iron offers a considerably greater resistance to 
compression than it does to extension, and the same 
may be said of the other metals. In a series of experiments 
made with a variety of metals, to test their properties 
in this respect, the several kinds did not differ so much 
from each other as might have been expected ; the metals 
employed were cast iron, wrought iron, and steel, and the 
specimens were in the form of short cylinders. The object 
for which the experiments were made was, to ascertain the 
force required to shorten a specimen, permanently, to the 
extent of y^o tn °f an i ncn ^ n tne direction of the length. To 
produce this amount of shortening required a stress which 
was found to range between 30,500 lbs. and 40,700 lbs. 
per square inch of area, the length of the specimen ope- 
rated upon, in each case, being 1 inch and the diameter 
•533 inch. This was not the force required to crush the 
specimen into a cake, or into fragments, which is not the 
point which it is of greatest practical importance to ascer- 
tain. For practical purposes, we require to know the pres- 
sure at which the surface of the specimen begins to yield 
or give way, and this pressure or stress is termed the elastic 
limit in compression ; ceteris paribus, that is the best mate- 
rial which requires the greatest pressure to produce the 
result. 

Of ten specimens, cut from cast-iron guns of high quality, 
the softest was found to yield with 30,000 lbs., while the 
hardest specimen was able to sustain 40,300 lbs., and the 
average resistance of the ten specimens was about 35,000 
lbs. Of ten specimens of wrought iron, cut from forgings of 
high quality, the softest began to yield with 22,800 lbs, 
and the hardest with 31,000 lbs., the average being 26,900 
lbs. In each case weight was added until the specimen 
became shorter, by the -j-^y-g-th of an inch. 

Table No. III. gives the compression and { sets ' with 10 



Cast Iron. 



41 



feet bars of cast iron; the bars were prevented from bending 
or buckling, by means of a case or mould in which they 
were contained. 

Experiments on compression of cast-iron bars 1 inch 
square and 10 feet in length : — 

TABLE III. 







Compressions 




Ratio of ■ 


Weights 






Sets in 


weight to 






Fractions of 
an inch=c. 


Fractional 

parts of 
the length. 


fractional 

parts of an 

inch. 


compression 
w 
c 


in lbs. = w. 


in tons. 


206474 


•9217 


•O1875 


1 

6394 


•OOO47 


IIOI20 


4129-49 


I -8 4 


•O3878 


1 
3091 


•00226 


IO6485 


6194*24 


2-76 


•05978 


1 
2007 


•OO4 


IO3617 


8258-98 


3-68 


•07879 


1 
1523 

1206 


•O0645 


IO4823 


1032373 


4-60 


•O9944 


•O0847 


IO3819 


12388-48 


5'52 


•12030 


1 
997 


•OI0875 


IO2980 


14453 '22 


6-44 


•I4163 


1 
847 


•OI405 


IO2049 


16517-97 


7-36 


•16338 


1 
734 


•OI7I2 


IOII02 


18582-71 


8-28 


•I8505 


1 
648 

581 


•0205 1 


IOO42O 


20647 -46 


9-21 


•20624 


•O2484 


IOOII4 


24776-95 


11-04 


•24961 


1 
480 


•0322 


99263 


28906-45 


12-88 


•29699 


1 
404 


•043 


97331 


33030-80 


1472 


•35341 


1 
339 


•06096 


93463 


37I59-65 


16-56 


•41 149 


1 

291 


•0842I 


90304 


Bar much 












undulated 












Limit of ela 


sticity, ^ 


of weight w 


hich perm 


anently injui 


•ed the bar. 



Table No. IV. is also from the Report of the Commis- 
sioners j and from the Tables here given, together with the 
other results of experiments referred to in this chapter, the 
nature of cast iron may be approximately inferred, at least so 
far as regards its more prominent characteristics. 



42 



On the Strength of Materials. 



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Cast Iron. 



43 



The following Table refers to experiments, made at Wool- 
wich, with short cylinders of soft cast iron under compres- 
sion : — 

TABLE V. 

Length of specimen, I inch j diameter, '533 of an inch. 



Weight applied 

per square inch 

into tons. 


Compression in decimals of an inch. 


Elasticity as 
shown by differ- 


Visible. 


Permanent. 


visible and perma- 
nent compression. 


3-8 
no 
17-6 
20 -6 
50*0 


•003 
•004 
•006 

•007 
crushed 


•OOO5 
•OOI 
•002 
•OO25 


•OO25 
•OO3 
•OO4 
•OO45 



The stress required to produce a complete crushing of 
the specimens is shown by the two following Tables : — 



TABLE VI. 

Experiments on the crushing strength of Cylinders of Cast Iron, made 
by Eaton Hodgkinson, Esq., for the Commissioners. 



Description 

of 

Iron. 


Diameter 
of specimen 
in inches. 


Height 
of specimen 
in inches. 


Mean crushing 

weight per square 

inch of section 

in tons. 


No. of 

Experi- 
ments. 


16 various 
sorts 


75 

75 


75 
i-5 


39-37 
38-28 


48 
48 



By reducing a number of other experiments to a common 
form, we obtain the following results : — 



44 



On the Strength of Materials, 



Abstract of various Experiments on the Crushing Strength of Short 
Cylinders of Cast Iron. 



Authority. 


Nature of Iron. 


Mean crushing 
weight weight 
per square inch. 


Hodgkinson for 

Commissioners 

Fairbairn . . 

Do. . . 

Do. . . 


From various parts of the king- 
dom 

Carron, hot blast, No. 2 . . 

Carron, cold blast, No. 2 . . 

f No. i Iron, from various parts 

of the kingdom 

j No. 2, do. do. do. 
l^No. 3, do. do. do. 


38-8 
54V35 
55*975 vo 

40*118 1 $ 

42-68 f § 

58-675J | 

! 



The following abstract, from the researches of Sir William 
Fairbairn, C.E., Bart., shows the gain or loss of strength from 
remelting cast iron : — 

* Abstract of experiments on the crushing strength of the 
same iron, after successive remeltings : 

' Decreased in strength from 44 to 40*17 tons, by remelt- 
ing four times, then gradually increased from 40*17 at the 
fourth remelting to 95*9 tons at the fourteenth remelting.' 

' Abstract of experiments on the transverse strength of the 
same iron, after successive remeltings : 

* Increased in strength and elasticity up to the twelfth 
remelting, and then gradually decreased in both properties 
from the twelfth remelting until, after being remelted eighteen 
times, it only possessed f ths of its original strength, and the 
ultimate deflection of the bars had decreased from 1*44 to 
•476 inch.' 

The following Table contains results of experiments, on 
the transverse strength of cast iron, "at various temperatures, 
by Sir W. Fairbairn. It may be useful to note the nth ex- 
periment, such exceptional results are constantly met with 
in practice : — 



Cast Iron. 



45 



TABLE VII. 

These results are reduced to i inch square, and 2 feet 3 inches between 
the supports. 



Nature of Iron. 


Temperature. 


Breaking weight 
in lbs. 


Relative power of 
resisting impact. 


Cold blast 
No. 2. 


27° 
32 
113 

192 

red in dark 

red by daylight 


874-0 

949 -6 
812-9 

743*1 
723-1 

663-3 


5977 
382-4 
273-1 
223-7 


Hot blast 
No. 2. 


20 

32 

84 

136 

187 

188 

red in dark 


8117 
919-7 

877-5 

8757 
638-8 
823-6 
829-7 


325-0 
395'° 
369-4 
340-6 
229-3 
298-9 


Hot blast 
No. 3. 


212° 
600 


814-4 
875-8 


— 


Cold blast 
No. 3. 


212° 
600 


924-5 
1033-0 


— 



These experiments teach us, first, that No. 2 cast iron is 
stronger at the freezing point to resist transverse strain and 
impact, than at any other temperature, and that when the 
temperature is raised from 32 to 113 , the cold blast iron 
loses 14*4 per cent, of its transverse strength, and 28-5 per 
cent, of its power to resist impact. Secondly, that the No. 3, 
or hard irons, are stronger at high temperatures than at 
lower ones, apparently the reverse of the result with the 
No. 2 iron ; this, however, is probably owing to the increased 
ductility of these irons at the higher temperatures. 



On the Strength of Materials. 



CHAPTER V. 

WROUGHT IRON. 

The material most extensively used in the arts is the mal- 
leable, ductile, tough, fibrous, weldable material, usually 
termed malleable or wrought iron. This variety of iron, at 
the present time, is made directly from cast iron, by a pro- 
cess of elimination, whereby the greater portion of its car- 
bon, as well as any sulphur, silicon, phosphorus, and other 
impurities are got rid of, as far as may be practicable, the 
change being effected by subjecting the iron, while in a hot 
or liquid state, to the oxidising influence of a powerful 
flame, by which the impurities, as well as the carbon, are 
carried away in the form of gas or combine with the slags 
in the furnace 

This purification of cast iron gives the mass an entirely 
different nature and new characteristics. By the process, it 
becomes considerably stronger, it acquires a great degree of 
toughness, yet, unfortunately, it loses the capability of being 
cast in moulds. As a compensation, it acquires a new 
property, namely, the quality of assuming the viscous or 
sticky condition, so that when two or more pieces are 
brought together at the proper temperature, they may be 
united by the welding process, as it is termed, either by 
the blows of a hammer, by pressure, or otherwise. 

When cast iron is thus acted upon by an oxidising 
flame, and every part is exposed to its influence in the 
puddling process, the newly-converted mass of viscous iron, 
when removed from the furnace, may be compared to a 



Wrought Iron. 47 

dirty iron sponge full of impurities, the doughy mass has 
to be put under a steam hammer, or some form of 
squeezer, in order to drive or wring out the mechanical 
impurities which it contains. It is then elongated, by means 
of rolls, into a rough bar and cut into short pieces ; these 
pieces are piled up into a bundle, which is reheated to the 
welding point, and again rolled, so as to cleanse the iron 
thoroughly. Indeed, for the better descriptions of wrought 
iron, the processes of piling, reheating, and rolling are some- 
times repeated several times, until the proper quality is 
attained. 

The quality of wrought iron thus treated depends, to a 
great extent, on the original selection of the mixture of cast 
iron from which it has been made, as well as on the purity 
of the fuel used for the converting process. Iron has an 
inherent and great affinity for sulphur, phosphorus, or other 
impurities, which it has the opportunity of taking up ; hence 
wrought iron of high quality can only be obtained by extreme 
care in every stage of its manufacture. 

In the manufacture of those qualities of wrought iron 
in which purity is the most essential condition, mineral fuel is 
dispensed with, and charcoal made from wood is employed 
as a substitute. Such wrought iron is chiefly used for sub- 
sequent conversion into the better qualities of steel, by 
means of the process of cementation. 

By whatever process the change from cast iron into 
wrought iron is effected, the decided alteration of the whole 
character for the better is unmistakable, and that the ulti- 
mate tensile strength should be increased to an average 
of 25 tons per square inch, and the limit of elasticity 
to 10 tons per square inch, by the elimination of car- 
bon and other impurities, are very remarkable facts. 
Wrought iron is found to differ almost as much in quality 
as cast iron, and this is partly due to the fact, that it 
is seldom or ever entirely free from carbon or other ingre- 
dients. The amount of carbon varies from an impercepti- 



48 On the Strength of Materials. 

bly small quantity up to \ per cent., wrought iron contain- 
ing the latter proportion being almost equal to mild steel. 
The presence of a small quantity of carbon, while serving 
to increase the strength, rigidity, and hardness of the ma- 
terial, at the same time greatly interferes with the welding 
property ; for this reason, it is much more difficult to weld 
the stronger or more steely kinds of wrought iron, than the 
softer, weaker, and less steely varieties. Pieces of soft 
iron go together, and unite into a homogeneous mass much 
more kindly than harder and less pure pieces, when 
raised to the welding temperature. The quality in this 
respect is easily ascertained, by making the iron red hot and 
plunging it into cold water, when the soft iron is found to 
retain its softness, but the hard iron becomes still harder, 
in a manner similar to the behaviour of steel, though in a 
less degree. 

The production of large masses of cast iron, by melting the 
metal, is much more easily accomplished than the process 
of welding similar masses of wrought iron ; in the former 
case the founder has simply to prepare an earthy or other 
refractory mould, to provide due means for its ventilation 
at the moment of casting, and then to pour out the fluid 
metal, which finds its level and fills up the empty space, 
in the same manner as water, when poured into a vessel. 
But, in the formation of large masses of wrought iron by 
forging or welding, the operations are of a slower and 
more expensive nature than those of the founder. The 
process of forging is a kind of gradual building up, bit 
by bit, variously conducted, to suit the individual circum- 
stances of each particular case. In a general way, the 
operation of building up large masses of wrought iron, is 
accomplished by uniting an innumerable number of small 
pieces into blooms ; then a number of blooms are united into 
slabs and smaller slabs into larger ones, until at length the 
ultimate dimensions of the required forging are attained. 
When it is borne in mind that a sound weld depends not 



Wrought Iron. 49 

only upon the purity and equal temperature of the surfaces, 
but likewise upon the absence of all vitrified oxide, dirt, or 
impurity of any description between the parts to be joined, 
it is manifest that the forging of immense masses of wrought 
iron is an operation surrounded with many practical difficul- 
ties, and its application, for purposes where perfect homo- 
geneity of mass is essential, is therefore limited. It is, also, 
too often found that the excess of heating, in proportion to 
the hammering or working that can be given to the mass, 
is injurious, and that, consequently, the iron of the heavy 
forging is reduced in strength, when compared with the 
original iron, in the condition of rolled bar. 

RESISTANCE OF WROUGHT IRON IN TENSION. 

The ultimate tensile strength of wrought iron is usually set 
down as 25 tons per square inch, but this is above the 
present general average, 23 tons being nearer as an ap- 
proximate round number. At the same time, hard steely 
wTOught iron frequently has a tenacity of 30 tons, and inferior 
kinds of only 19 tons. As a rule, square or round bars are 
stronger than plates, by at least 3 tons to the square inch, 
but weaker iron is not inferior for some purposes; such 
iron frequently has the welding property in a marked de- 
gree, and is preferred in consequence, wherever welding 
has to be extensively resorted to, in converting wrought 
iron into the required articles. 

Entire specimens, cut from a rough bar of wrought iron 
as it leaves the rolls, are generally found to be weaker 
than a portion of the same bar, which has been turned in a 
lathe before testing. If a portion of the same rough bar is 
hardened by any mechanical process, such as cold rolling, or 
swaging or hammering, the strength and hardness are both 
increased, but by annealing the specimen, the original con- 
ditions of strength and softness are fully restored. 

In the process of rolling iron into bars or plates, the 
molecules and aggregates of molecules of the iron are elon- 

E 



50 On the Strength of Materials. 

gated into what is usually termed fibre. It might, there- 
fore, be expected that the bar or plate would be stronger 
when drawn asunder, with the tension in the direction of the 
fibre, than when drawn asunder, with the tension at right 
angles to the fibre. There is, however, comparatively 
little difference, unless the mass is thin, as in plates ; the 
chief difference, shown in experiments, is that the elongation 
of the bar by the strain is greater in the former case than in 
the latter, and an earlier warning is given of the impending 
fracture. 

The strength of wrought iron, as given in the older tables, 
ranges higher than would be the case if similar tables were 
now to be compiled, from specimens taken at random from 
the iron of commerce. Wrought iron has been quoted to 
have a tenacity of 34 tons, but unless the experiments giving 
that tenacity were inaccurately earned out, the iron must 
have been hard and steely ; we still find wrought iron . occa- 
sionally with a tenacity of 30 tons, and the writer has some 
specimens of 32 tons, but such iron is hard and almost 
unweldable, and is much more brittle than iron of a lower 
tenacity ; hence, in selecting iron for any particular purpose, 
the peculiar strains to which it will be exposed must be taken 
into consideration, before determining the quality which 
should be employed. 

The strength of wrought iron is not much affected by 
variations in temperature, when under 350 Fahr. ; above that 
temperature, it begins to lose strength, and as it approaches 
to a dull red heat, the ductility greatly increases, and the 
flowing property comes into play and reduces the resistance 
fully one-half; hence the opportunity for the smith to ' strike 
while the iron is hot.' 

There has been considerable difference of opinion, in 
regard to the strength of wrought iron when exposed to severe 
frost, but, from recent investigation, it would appear that prac- 
tically it is not much, if in any appreciable degree, affected 
by the lowest temperature of an English winter. Never- 



Wrought Iron. 5 1 

theless, there exists a popular notion that iron and steel are 
greatly affected by frost, and thereby rendered more brittle 
than when at an ordinary temperature, and this notion re- 
ceives some support from the fact, that the fracture of rails 
and railway axles is most frequent in winter. But the fact 
is susceptible of another and more probable explanation, for 
in winter the roads are hard and rigid, causing great jar. 
The notion that the strength of iron is less in cold weather is 
not borne out by the general average of the experiments made 
in summer compared with the average of those made in 
winter ; these experiments, however, are performed within a 
building. 

That wrought iron is to some extent more ductile in 
warm weather, than in extremely cold weather, seems pro- 
bable, even, although the tenacity is not much affected. 
This effect of the presence of heat may also, in some degree, 
justify the general belief which exists amongst practical 
men, of the greater liability to fracture in winter than in 
summer. It is frequently found, when guns are being proved 
to destruction by continued firing, that the first round in 
the morning, when recommencing the experiments with a 
cold gun, proves fatal to its endurance. 

The appearance which is presented by a fracture of 
wrought iron depends greatly on the mode in which the 
rupture has been effected. If it is accomplished suddenly, 
the fibre is actually broken short, and the crystalline tex- 
ture apparently predominates ; whereas, if the fracture is 
produced by a slower process, the fibre of the bar is then 
made conspicuous, because the element of time is essential 
to enable the fibres to be drawn out from each other. All 
such appearances, however, are greatly modified by the 
quality of the bar which is operated upon; some judgment, 
as well as experience, being necessary to arrive at a just 
conclusion, and opinions formed from the fracture only are 
not always to be depended upon, even when the examina- 
tion is made by an expert. 

E2 



52 On the Strength of Materials. 

From many fractures of wrought-iron axles, chains, and 
other pieces, which have been in daily work for a number of 
years, the idea has become general, that with sufficient 
intensity of jar, repeated an indefinite number of times, a 
change takes place in the structure of the iron. This is not 
inconsistent with the results obtained by the testing machine. 
It is satisfactory to know, however, that such a result may 
in a great measure be anticipated and prevented by simply 
Subjecting the axle, chain, or hook, from time to time, to 
the process of annealing, by which its original condition 
is practically restored. 

At the same time, it may be stated that this is an obscure 
subject, for there is not much positive evidence of the fact, 
or explanation of the cause of such deterioration in wrought 
iron, after being exposed to long-continued working, as in 
the axles of railway carriages and in crane chains • still, 
if such is the case, it is now generally considered to be due 
to the effect of vibrations often repeated, when the part 
affected is for the moment loaded up to or beyond the 
elastic limit. For it has to be remembered that, in the case 
of the crane when surging, or in that of a carriage jolting, 
this element of motion suddenly checked produces a stress 
which has to be added to the ordinary stress existing 
when the several parts are in a state of rest. Cranes that 
are usually worked with less straining than that for which 
they were originally intended, seem to maintain their effi- 
ciency for an indefinite period, whereas other cranes, which 
are much employed up to their maximum ability, do some- 
times give way unexpectedly, and with a less load than that 
to which they have been usually subjected. In some cases 
there is an excess of deflection on a particular part, which, 
being often repeated, has ultimately 'caused fracture. 

Whatever may be the explanation, the phenomenon 
is now familiar to those who are engaged in practical 
operations, that when a piece of wrought iron is thus sub- 
jected to a long-continued series of blows, or violent jars, 



Wrought Iron. 5 3 

of sufficient intensity, or that call the full elasticity of the 
material into active exercise, rupture will sometimes take 
place prematurely, and must be expected sooner or later. 
The change to rigidity, which overtakes iron when worked 
cold, may partly account for some of the frequent fractures 
of the chains of cranes or other iron-work similarly ex- 
posed, and this view is in some measure supported by 
the fact that when such chains are annealed, at stated in- 
tervals, say annually, the liability to accident is greatly 
diminished. 

Considerable difference of opinion and practice exists 
with regard to the safe load which may be put upon ordinary 
wrought iron ; this of course must depend greatly on the 
nature of the structure, and the kind of stresses to which it 
is exposed. A crane, for example, with the risk of a load 
being suddenly checked, during lowering, by a rash attendant, 
must necessarily have a larger margin of safety than would 
be required for a structure with a steady load; for the latter, 
a strain of 5 tons might be ventured with safety, while for the 
former 2 J tons would hardly afford the same measure of 
security; some judgment has therefore to be exercised in 
determining the strain that wrought iron may be entrusted 
with, but in no case should it be burdened with a load 
producing a strain of more than 5 tons per square inch of 
sectional area. 

Wrought iron is frequently found to present peculiar 
phases of character, which must not be overlooked, as the 
conditions affect its strength ; some descriptions of wrought 
iron, otherwise good, are found to be intractable and appa- 
rently brittle when red hot, yet are perfectly pliable when 
cold — this peculiarity is usually considered to be due to the 
presence of a small trace of sulphur in the iron. Then 
there are other descriptions of wrought iron having the op- 
posite quality, being comparatively brittle when in the cold 
state, and perfectly pliable and workable when red hot. This 
quality is said to be due to the presence of silicon or phos- 



5 4 On the Strength of Materials. 

phorus. These conditions are so marked as to suggest the 
idea that the gas of the impurity forms a coating, which 
envelopes or separates the molecules of the iron, and they 
greatly diminish the value and usefulness of the iron in 
which they exist, for many practical purposes. These defects 
are mostly due to the impurity of the original ore, and the 
ironworker usually corrects them in the course of manufac- 
ture, by combining ores of opposite nature in suitable pro- 
portions, so as to obtain an average quality ; of these two 
defects the ' red shortness/ as it is commonly termed, is 
the less objectionable. 

In wrought iron, and especially that of high quality, 
there is no fixed point at which permanent set begins to be 
observed ; for although we speak of the limit of elasticity as 
somewhere in the vicinity of 28,000 lbs. per sq. in., or about 
half the ultimate tenacity, yet, at the same time, it has to be 
clearly realised by the student that such a statement is only 
approximate ; and although round numbers may be easily 
remembered, and are sufficiently correct for most practical 
purposes, still they must be considered as approximate 
only, and taken with reference to the exact truth contained 
in the following Tables. The student is referred more espe- 
cially to Table VIII. , which throws more precise light on 
the facts than any general statements. 

It has also to be observed that in making experiments, 
whether with long or short specimens, there is a marked 
difference between the behaviour of cast iron and wrought 
iron. It has been already stated that the former has com- 
paratively little perceptible elongation, unless the bar is of 
considerable length, while the elongation of the latter can be 
•seen distinctly, and increases even to the last moment. The 
final stress which is required to produce rupture must not 
be calculated from the original dimensions of the specimen. 
The final stress is the actual strength of the reduced area 
after stretching. This stretching is one of the distinguishing 
features of wrought iron as compared with cast iron, and is 



Wrought Iron. 5 5 

one of the special virtues of good wrought iron and mild 
steel. 

When wrought iron is wire-drawn and its section reduced, 
the strength of the part so elongated is increased by 
the process. Thus, an iron wire, when made with iron of 
a strength of 25 tons, will have its tenacity increased to 
35 tons per inch of sectional area by the mere process of 
drawing ; and the most remarkable feature of all is this, that 
the specific gravity is actually reduced at the same time, show- 
ing that the conditions which give strength are not solely 
dependent on the closeness of the molecules. 

In the former part of this chapter attention has been drawn 
to different qualities or natures of wrought iron. When a 
variety of specimens of different kinds of wrought iron are 
under great tension, their respective behaviour will greatly 
depend on their own inherent hardness or softness ; a 
hard specimen will be found to elongate very little, and 
will ultimately fracture without reduction of diameter, while 
a softer specimen will be drawn out considerably, the 
middle part becoming gradually smaller, and fracture will 
ultimately take place at the smallest section, most probably 
at a lower strain than was the case with the harder iron. It 
might then be inferred, that the hard iron was the better of 
the two ; but such an inference might not be correct, as 
the latter would, practically considered, be much more 
reliable when subjected to jar or sudden strain. At the 
same time, in estimating the original strength of the elon- 
gated specimen, it will be objectionable to take the reduc- 
tion of diameter into consideration because for practical 
purposes the elongation should never be called into exer- 
cise. The advantage of soft iron is, rather that it can be used 
with greater safety, than that a higher stress can be permitted 
where it is employed, for the softer iron is more likely to 
be drawn out than to be broken asunder, and gives ample 
warning before ultimate fracture. 

In experiments made at Woolwich with ten short speci- 



56 On the Strength of Materials. 

mens, cut from heavy wrought- iron forgings, the average 
apparent limit of elasticity was only 23,760 lbs., while the 
average point of ultimate fracture by tension was equal to 
48,160 lbs. The forgings from which the specimens were cut 
were all intended for gun purposes, and consequently were 
of high quality, or intended to be so. Similar experiments 
were made with rolled bars of the same high quality, both in 
the state of bars and when wound into spiral coils, and then 
subjected to the welding process, in order to form them 
into entire cylinders for gun manufacture. All the specimens 
were found to have suffered from forging, to the extent of 
3,481 lbs. per square inch, on an average. The results were 
as follows : — 

Limit of elasticity < n , * * n 

I Cylinder . . . 27,852 ,, 

. Ultimate rapture (*" , 58,986,, 

I Cylinder . . . 55,500 „ 

No doubt, the loss of strengtn here shown was owing to 
the absence of sufficient working, to counteract the weak- 
ening tendency of excessive heating. 

From some interesting experiments, that were made to 
ascertain the tenacity of the welds of different qualities of 
iron, and with differently formed welding surfaces of contact, 
it was found that with soft iron of the finest quality, heated 
in a clear fire, with scarfed joints, and both surfaces slightly 
rounded, the strength of the welds was equal to that of the 
original bar, or in round numbers about 25 tons per square 
inch ; while with other descriptions of harder iron, variously 
selected, the strength of the welds was always less than that 
of the bars, the lowest and worst example, which was an 
exceedingly hard and steely specimen, having a tenacity at 
the weld of only 12,000 lbs. per square inch. A still lower 
average result was obtained in all attempts at butt- welding, 
with similar qualities of iron, even when the surfaces were 
rounded to give a clearway of escape to the vitrified oxide ; 



Wrought Iron. 57 

the average ultimate tenacity was 3 2, 140 lbs., or a little over 
half of the strength of the iron. With turned butt surfaces, 
when heated in a furnace flame, it was a little higher than 
the above. 

Some experiments were made with bar iron of a very hard 
steely quality, its ultimate strength being about 30 tons, 
in the specimens cut from the bar. It was, of course, 
difficult to weld such iron, and impossible to secure butt 
welds with a tenacity greater than 10,000 lbs. per square 
inch, the steely property, due to the presence of carbon, 
being the barrier to a ready union of the pieces, when 
manipulated by the smith in the ordinary manner. It will 
thus be seen that the strength of a wrought-iron structure 
depends on many conditions, all of which have to be taken 
into consideration in estimating the reliance to be placed 
on it, or in calculating the requisite quality or quantity of 
material to be employed. 

Table VIII. is a synopsis of the results of an experiment 
made to show the extension and permanent set of a rod 
of wrought iron 50 feet long, and which have been reduced 
in this Table so as to compare with the other experiments, 
of a similar nature, but made upon a rod of cast iron 1 o feet 
long, as given in Tables II. and III. 

Column No. 1 shows the relative value of the successive 
weights that were used in making the experiment, and is 
inserted for comparison with the relative value of the exten- 
sions that were produced by those weights, as shown in 
column No. 4 ; by means of this comparison will be seen 
the departure from a constant uniformity which might be 
expected. 

Column No. 2 gives the actual weights in lbs. which were 
applied per square inch of section of the rod. 

Column No. 3 gives the actual weights applied per square 
inch of section of the rod in tons. 

Column No. 4 shows the relative value of the extensions 
produced by the successive weights, and teaches when 



58 



On the Strength of Materials. 



00 








'Oglo£z UB3J\[ 


■ 

Ratio of th 

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per square in 

to the 

extension. 


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t> 


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length in 

inches. 


perceptible 

•0005 

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inches. 


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Relative 

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Relative 
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m N ro^j- vr,\© f»»CQ On O -* W co tt "">vO r^ 



Wrought Iron. 



59 



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Wrought Iron. 61 

compared with column No. i — first, that the elasticity of 
wrought iron as here shown is not so perfect as is generally- 
assumed, even when the strains to which it has been 
subjected are small. If the material had been perfectly 
elastic, the relative value of the extension would have 
corresponded, exactly, with the relative value of the weight 
applied, that is to say, twice the first weight applied would 
have produced twice the extension caused by that weight ; 
three times the weight, three times the extension, and so 
on ; but this is not the case. Second, that there is only 
a slight and gradual increase in the relative value of the 
extensions over that of the weight applied, until that weight 
exceeded twenty times the first weight applied, and when 
the material was subjected to a stress of 11*26 tons per 
square inch, or about one-half the ultimate strength. Third, 
that after this point is reached, the value of the extension 
produced exceeds the relative weights very rapidly, until 
when the rod is subjected to a stress of 16*33 tons P er 
square inch for six minutes, it is stretched seventeen times 
more than it would have been if the material had been . 
perfectly elastic. 

Column No. 5 gives the actual extensions, and shows very 
clearly — first, that the length of time during which the mate- 
rial is subjected to a stress, has a considerable effect upon 
the result. To take an example from the Table, with a weight 
of 1 3 -52 tons, or rather more than one-half the breaking 
weight of good wrought iron, the extension on 10 feet of 
length increased from "1991 inch, when the weight was first 
applied, to -2366 inch, after the weight had acted upon the 
rod for seventeen hours. Second, that by removing and 
replacing the same weight the extension is increased. (This 
is not observable to the same extent in testing short spe- 
cimens.) 

Note. — In each of the above cases it will be observed that 
the weight is more than one-half the ultimate breaking load. 

Column No. 6 gives the extensions produced in fractional 



62 On the Strength of Materials. 

parts of the length, and will be found to be useful for ascer- 
taining the extension of wrought iron of any length by the 
application of any of the weights, per square inch, given in 
the Table. 

Column No. 7 gives the amount of permanent set pro- 
duced by the successive weights, and teaches — first, that 
with so small a weight as half a ton per square inch, a per- 
ceptible set was given to wrought iron; second, that the 
amount of set was very small, until the material had been 
strained up to one-half its ultimate strength, or about 11-26 
tons per square inch, at which point the set was -0068 or 
■^3-rds of the extension • third, that the set rapidly increased 
after the stress had reached 11*26 tons per square inch, or 
one-half the ultimate strength, and when it reached 14*08 
tons or about f ths of the ultimate strength, the set amounted 
to T083 inch or fths of the extension, and when strained 
to 1576 tons per square inch, or less than f of the ultimate 
strength, the set was nearly T 9 oths of the extension produced 
by that weight. 

Column No. 8 only shows a comparative result, and the 
numbers there given are obtained, by finding the ratio of 
the weight applied in lbs. to the extension produced in 
inches, and had the numbers in this column been equal, 
then the material would have been perfectly elastic • but 
although not equal, yet the numbers in the first twenty ob- 
servations are nearly so, and therefore show that the material 
was near to perfect elasticity under strains less than 11*26 
tons per square inch • hence, we infer that the usual expres- 
sion of * the limit of elasticity ' is admissible, and in the case 
of wrought iron is almost correct. 

The mean of these twenty numbers is 230,760, and con- 
sequently the extension of this bar of wrought iron in inches 
may be taken at -2 sw^o-th °f tne weight applied in lbs. to 
stretch it, and the weight applied in lbs. to produce any 
given extension would have to be 230,760 times the ex- 
tension in inches. Now the modulus of statical elasticity 



Wrought Iron. 63 

is generally understood to be the weight or force in lbs. 
which would stretch a bar to double its length, if its elasticity 
remained perfect, and as this Table shows the extension on a 
bar 120 inches long, we obtain the modulus when we find 
the weight required to stretch this bar 120 inches, namely, 
230,760 x 120=27,691,200 lbs. 

Note. — This number is variously stated in books upon 
the subject, and would be greater or less than that given 
above according as the material employed was more or less 
elastic. 

It would have added to the value, and probably would 
have modified the results, if the expansion and contraction, 
due to the differences of temperature, had been taken into 
account, which does not appear to have been the case, 
judging from the description given in the Blue-book in 
which they are recorded. 

RESISTANCE OF WROUGHT IRON IN COMPRESSION. 

In the manifold structures for which wrought iron is now 
so extensively applied, the property of resisting compression 
is frequently called into active exercise. Whenever wrought 
iron is thus subjected to compression, in either large or 
small structures, a permanent deformation is produced, if 
the load exceeds a certain value. It may be seldom that 
the liability of this metal to give way by compression is 
observable, as compared with failure in tension, because 
the failure in the former case is more likely to occur 
from flexure or want of stiffness, which again may be due 
to want of fixedness. In structures subjected to thrust, 
much depends on the mode of attaching the several parts, 
such as struts or stays, to the adjoining parts. A great 
improvement has taken place of late years in this respect ; 
the extensive employment of the lathe, planing-machine, and 
other refined tools, extensively used in modern workshops, 
permits the parts which have to be joined to be truly faced at 
the ends, so as to take the correct position firmly; and this 



64 O11 the Strength of Materials. 

can be done at such a moderate cost as to render it com- 
mercially practicable. The sound and uniform bearing at 
the connection, thus obtained, adds greatly to the strength 
of the whole structure. By secure fixing, the work to be 
done on the material, in order to cause it to deflect, is 
considerably more than doubled, without increasing the 
weight. 

Referring to page 40, there are quoted certain experiments 
with wrought iron and cast iron as agents to resist com- 
pression, from which it will be seen that the stress necessary 
to shorten certain specimens of good wrought iron an 
amount equal to T ^ ¥ ths of an inch was, for the softest 
22,800 lbs., the hardest 31,000 lbs., the average being 
26,900 lbs. 

' The foregoing experiment was made with specimens cut 
from forgings. From experiments made with ten other spe- 
cimens taken from rolled bar iron of high quality, the speci- 
mens having been reduced in a lathe from 3-inch bars, the 
softest specimen required 31,000 lbs., and the hardest 
35,000 lbs., or an average of 33,000 lbs. It will be ob- 
served, that the iron of the bar was considerably superior 
to the iron cut from the forging, although the two were of 
similar quality originally, thus showing the effect of better 
working. 

Table IX. contains the results of a number of experi- 
ments carried out at Woolwich with short cylinders of 
wrought iron under compression. 

Structures scarcely ever fail practically from the actual 
crushing of the material ; failure is more often due to the 
alteration of form which takes place, disturbing its fit- 
ness for the particular purpose for which it is intended. 
When the pillar, strut, or frame, is long, it generally 
yields by flexure rather than actual crushing. If pro- 
perly stayed or trussed at intervals, a long rod will act 
as a pillar, taking the stress through the entire length, the 
elasticity being uniform throughout. But in order to save 



Wrought Iron. 

TABLE IX. 

Diameter of specimen, -533 inch ; length, 



65 



inch. 



Nature of Iron. 


Weight 

applied in 

tons per 

square inch. 


Compression 
in decimals of an inch. 


Elasticity as 

shown by the 
difference 

between the 
visible and 
permanent 

compression. 


Visible. 


Permanent. 


Specimens cut from 
bar iron, varying 
from \ to 2j 
inches square. 


7-8 
u-6 
13*4 

I3'4 
158 
50-0 


•OOI5 

•OO25 
•OO45 

•0055 
•OO75 


•003 

•OO35 
•0055 
•245 


•OOI5 

■OO25 
•OOI5 
•002 
•002 


no 
12-4 
14-0 
15-0 
160 
50-0 


•002 
'OO3 

■OO45 
•0065 
•OO75 


•OOO5 

•002 

•OO35 

•005 

•26 


•OO25 
•OO25 
•OO25 
•OO25 


12 *o 
13-2 
14-0 
150 
16-0 
50-0 


•OOI5 

•OO25 

•004 

•006 

•008 


•OOO5 

•OO15 

•OO35 

•006 

•245 


•OOI5 

•002 

•OO25 

•OO25 

•002 


14-4 
14-8 
50-0 


•OO25 


•005 
•007 
•259 


•002 


Marshall and Mill's 
Irons, soft and of 
fine quality. 


n-8 
12 -o 
126 

13-2 

50-0 


not noted 


•003 

•OO35 

•004 

•OO45 

•2655 




14-4 
15-0 

15-6 
160 
50-0 


•OOO5 
•OO25 
•004 

•0055 
•2615 


10 -o 

II'O 

50-0 


•OOO5 
•OO25 
•OO45 
•286 



66 



On the Strength of Materials. 



Table IX. — continued. 



Nature of Iron. 


Weight 

applied in 

tons per 

square inch. 


Compression 
in decimals of an inch. 


Elasticity as 

shown by the 

difference 

between the 
visible and 
permanent 
compression. 


Visible. 


Permanent. 


Taylor Brothers' 
Yorkshire Iron ; 
in the direction 
of the fibre. 


n-8 

I2- 4 

13-2 

50-0 


not noted 


•002 
•OO35 

•0055 
•2775 




13-0 

14-0 
50-0 


•015 
•OO4 
•287 


14-0 

14-5 

50-0 


•OOI5 

•004 

•249 


S. C. Iron. 

Specimen cut 
from a welded 
coil. 


IO'O 

114 
50-0 


not noted 


•OOI 
•004 
•318 




IO'O 
1 1 2 
50-0 


•001 

•OO4 
•3I05 


n-8 

12-8 
50-0 


•OOO5 

•004 

•288 


12 -O 

126 
50 "O 


•OOO5 
•OO35 
•2845 


126 
14-2 

14-8 

50-0 


•OOO5 
•OO3 
•OO45 
•2565 



the expense and trouble of trussing or encasing long bars, 
when making experiments to ascertain the resistance to a 



Wrought Iron. 67 

crushing force, it is more convenient to deal with short 
specimens, otherwise deflection will commence before the 
molecules begin to flow. 

By increasing the stress upon these short cylinders of 
wrought iron or soft steel, they are found to shorten gradu- 
ally by bulging outwards in the middle. The effect of this 
change of form is to slightly stiffen the metal, and this 
affects the malleable or flowing property ; unless the speci- 
men is extremely soft, it will soon show symptoms of slight 
fissures or cracks at the part which is bulging. To prevent 
this, the annealing process must be resorted to, and with 
care the pillar can be flattened down to a thin disc, gra- 
dually presenting a larger surface for the machine to act 
upon. Reckoning the intensity of the ultimate pressure 
from the original dimensions, a stress of upwards of 100 
tons per square inch is necessary to actually flatten down 
wrought iron. 

'When wrought iron or steel is flattened by compression, 
it might be supposed that the specific gravity would be in- 
creased ; but such does not appear to be the case to any 
appreciable extent. The specimen either cracks and splin- 
ters, or finds relief by lateral yielding, the enlargement 
commencing in the middle of the cylinder. 



* 2 



68 On the Strength of Materials. 



CHAPTER VI. 

STEEL - 

The material termed steel is a nearly pure alloy of iron with 
a small portion of carbon. As a metal, it is closely allied 
both to cast iron and wrought iron, and may be made from 
either. 

The most common mode of manufacture is to convert 
pure wrought iron into steel, by measuring out a definite 
portion of carbon for the iron to absorb ; or, it may be made 
from cast iron by a reverse proceeding, namely, by the eli- 
mination of the carbon and impurities, allowing so much 
carbon to remain as will give it the required steely qualities. 

Although steel thus forms a connecting link between 
wrought iron and cast iron, it differs greatly from the latter, 
cast iron being a crude, indefinite, and impure alloy, while 
steel is a purified alloy, containing a definite percentage of 
carbon. 

Steels differ from each other in many respects, but more 
especially in regard to the degree of steeliness, and, within 
certain limits, any degree of steeliness may be obtained. 
In making fine steel by the cementation or common process, 
bars of pure wrought iron are enclosed in a fire-clay box, 
and surrounded with powdered charcoal. The whole mass 
is then kept at a red heat for a certain period ; the porous 
molecular structure of the iron is opened, and the car- 
bon vapour finds its way into the body of the iron. The 
bars of iron are subjected to this process for a period gene- 
rally ranging from five days to a fortnight, or even longer, 
according to the quality required ; the longer the process is 
continued, the more steely does the bar become. 



Steel. 69 

As some of the bars have a greater opportunity of 
absorbing carbon than others, and from other contingencies, 
the steeliness of the batch varies, and uniform quality can 
only be obtained by breaking the bars into small pieces, 
sorting these fragments into lots, judging by the appearance 
of the fracture, and then melting the lots in a crucible. 
The liquid steel is cast into an ingot, and hammered or 
rolled into the cast steel of commerce. In casting very large 
masses, a great number of crucibles are necessary, and as 
these must all be ready for pouring at the same time, and 
must be emptied into the mould consecutively, the successful 
casting of heavy ingots requires a very good organisation. 

In the arts, cast steel is required of all degrees of steeli- 
ness. The milder sorts of steel are only a little more steely 
than the harder varieties of wrought iron, and the mildest 
quality may contain about \ per cent, by weight of carbon. 
The highest qualities contain as much as 1 per cent, of 
carbon, and there are many intermediate qualities. As com- 
pared with hard wrought iron, mild steel, while not contain- 
ing much more carbon, is yet more perfectly homogeneous 
in its granular structure, and is superior to it both in 
strength, and in almost every other good quality. 

A good serviceable quality of steel, for many purposes, 
is now extensively made by the ' Bessemer ' process, which 
appears to be, at first sight, a reverse method to the cemen- 
tation system described above. The Bessemer process com- 
mences with cast iron in the crude state, which is melted 
and poured into a vessel, and, while liquid^ a strong current 
of air is passed through it. The carbon in the iron is 
burned out, by the oxygen contained in the air passing through 
the molten mass, and the other impurities are gradually 
eliminated, until at length the iron is in condition of com- 
parative purity, and chemically similar to wrought iron. In 
order to make it into steel, there is added to this purified 
metal, a measured portion of a pure cast iron, generally that 
called ' sfiegeleisen] or 'looking-glass iron,' containing a 



y-o • Strength of Materials. 

large and definite quantity of carbon, which converts the 
pure iron into a steel sufficiently good for an immense 
variety of applications. From the circumstance that steel 
may be produced by this process at a less cost than by the 
former method, it is, to a large extent, taking the place of 
wrought iron. 

Steel, like wrought iron, is much improved in its nature 
by being thoroughly worked either under the hammer or by 
rolling. Like most metals, steel is found to be more or less 
porous after casting, which is due to small air or gas bubbles 
which have not been able to find their way to the surface ; 
the effect of hammering or rolling is to consolidate the 
mass, and to render the grains of the metal finer, denser, 
and stronger. 

During the last few years, Sir Joseph Whitworth has been 
engaged upon a course of most valuable although most 
expensive experiments, conducted with powerful apparatus. 
These experiments have for their object, the attainment of 
steel of great density and general goodness, by combining 
the best materials and the most thorough working, and using 
every care that the best skill can devise. In Sir Joseph 
Whitworth's system, after the liquid steel is poured into a 
metal mould of sufficient strength, a piston or plug is in- 
serted, upon the top of which there is at once brought to . 
bear the full force of 8000 tons of hydraulic pressure. The 
effect is at once perceptible, a corresponding pressure per- 
vades the liquid steel, the porosity is overcome, and the 
metal shrinks rapidly by the sudden closing up of its pores. 
The shrinking continues for some time at a rate perceptible 
to the eye, and afterwards more slowly, for a period of 
nearly a quarter of an hour. Some of the shrinkage ob- 
served is due to the decrease of, temperature, but it is 
mainly owing to the hydraulic pressure. 

In considering the effect of pressure, as compared with a 
blow, in the consolidation of a mass of steel or iron, it would 
appear that the former should be the most effective, because 



Steel. J i 

the metal acted upon has not an opportunity of lateral yield- 
ing, whereas in either hammering or rolling, the metal flows 
away from the point of impact of the hammer, or squeeze of 
the rolls. Such is the view taken by Sir J. Whitworth. Hence 
when the ingot, which has been compressed in the liquid state, 
is taken out of the mould, it is brought to a working tempera- 
ture, and is then subjected to a series of squeezing operations 
by hydraulic pressure, squeeze after squeeze being applied 
until the required dimensions are arrived at ; this hydraulic 
pressure does not act without control, a dial and pointer 
shows the amount of compression of the mass, and so pre- 
vents any risk of over squeezing and making the article too 
small. The whole process is carried out with such ease, 
and is so gentle in its action upon the tools that are em- 
ployed, that on seeing the process performed, it is impos- 
sible not to feel that it is a great step in the right direction, 
and it is encouraging to find a man with the courage to go 
into such gigantic enterprises, for the purpose of advancing 
practical science. 

The goodness of steel may be said to depend on three 
things : first, the materials selected ; second, the nature of 
the working to which it is subjected ; and, third, the care 
taken by the makers. These three conditions apply to all 
descriptions of steel, from mild to high, and each quality is 
equally good for its own special applications. 

The quality of fine cast steel suitable for cutting tools, 
contains a larger percentage of carbon than either the milder 
varieties of cast steel, or the varieties of Bessemer steel, 
which are taking the place of wrought iron, or even the fine 
cast steel that is used for the lining of guns. The gun steel 
contains about "03 per cent, of carbon, and in its natural 
state has an ultimate tenacity of from 30 to 35 tons, but 
when made red hot and cooled in oil, its ultimate strength 
rises to 40 or 45 tons per square inch. The apparent elas- 
tic limit of short specimens rises in an equally remarkable 
degree, being for untempered steel specimens 13 to 15 tons, 



72 On the Strength of Materials. 

and for steel tempered in oil, 28 to 32 tons per square inch. 
The toughness is also increased, so that the tempered steel 
may be bent, twisted, or drawn out to a degree, far beyond 
that to which it would submit in the untempered condition. 

It will thus be seen that the limit of elasticity of mild cast 
steel, when tempered in oil, is fully equal to three times that 
of wrought iron. This is an important consideration, which 
will in time detennine the extensive use of that material, and, 
more especially, because it stretches so much before final 
rupture takes place, which is a very valuable and important 
property. 

The marked increase in the tenacity of cast or Bessemer 
steel, as compared with wrought iron, has already led to the 
application of the latter for many purposes where iron was 
formerly used, and wherever strength requires to be com- 
bined with lightness. In the case of rough structures, such 
as girders or bridges, the use of steel will gradually advance, 
the chief difficulty in the way of its more general application 
being, not so much the difference of cost, as the fact that 
the engineer is unable to determine whether good steel has 
been really employed by the contractor ; testing would settle 
the point, but the trouble and expense of testing every bar 
or plate is a serious practical barrier to the adoption of this 
■olan. It has been suggested that the specific gravity of a 
cutting from each part of a structure might be taken, steel 
being o-i per cent heavier than wrought iron, but the dif- 
ference is so small that the distinction of the quality by that 
test is rather too delicate for practical purposes. It has also 
been proposed to take some of the punchings from the 
plates, to draw them out to a small bar at a smith's forge, 
and to test them either for tenacity, or by tempering with 
fire and water in the usual manner. All such testing, how- 
ever, is not in accordance with the usual practical notions of 
the workshop at the present stage of our progress. 

In a wide range of experiments made with ordinary cast 
steel, when in its natural or untempered state, the ultimate 



Steel 73 

tenacity was found to vary from 114,000 lbs. down to 67,000 
lbs., the highest being a little over 50 tons, and the lowest 
a little under 30 tons per square inch ; but specimens of 
steel are often met with both of greater and of less strength 
than the foregoing. A cast-steel specimen of extreme soft- 
ness, cut from a Krupp gun, gave an ultimate tenacity of 
72,000 lbs., which is very remarkable when the extreme 
softness of the specimen is borne in mind. 

It might be inferred that the strongest quality of steel 
was always the best, but it is not so, the amount of tena- 
city which is desirable depends altogether upon the pur- 
pose for which it is to be used, the weaker and softer, or 
less steely qualities, being more tough, are preferred for 
many purposes, more especially for structures exposed to 
' vibration. 

The effect of tempering upon steel is to increase its 
strength, and, when the chill is rapid, to render it harder 
and more brittle. In tempering ordinary articles they are 
first heated to redness and then cooled in water, and there- 
by made over strong and over hard, and unfortunately very 
brittle ; these defects are then subdued by the application of 
a gentle heat, which is continued or increased until the 
required degree of temper is attained. 

The strength is determined by two things : first, the 
steeliness of the steel, that is, the proportion of carbon 
which it contains ; and second, the rate of cooling. The 
highest degree of strength is obtained by selecting a high 
steel, heating it to a dull red, and then chilling it rapidly. 
These two conditions give a degree of strength combined 
with toughness, far beyond that which is obtained by giving 
a higher degree of heat, then chilling it suddenly, and 
afterwards reducing the temper. 

When a block of mild cast steel is prepared for the 
interior barrel of a gun, it is desirable that all its properties 
should be known before it is put into the gun. Accord- 
ingly, two sets of specimens are cut from the block of steel, 



74 On the Strength of Materials. 

each set of specimens consisting of three pieces : the one 
set is used to find the best tempering heat for strength, 
elasticity, and ductility; the other set of specimens is used 
to find the best heat for toughness. One piece of each 
set is tried in its natural or untempered state ; one of each 
is tried after being raised to a high temperature and dipped 
into oil, and one of each is tried after being raised to a 
less temperature and dipped into oil. The three speci- 
mens of the first set, prepared as above, are turned in a lathe 
for the testing machine, and their several properties carefully 
noted. Then the three pieces of the second set are taken to 
suitable apparatus, and bent backwards and forwards, in 
order to ascertain the toughness of each of the three pieces. 
When all is concluded and the results noted, a careful con- 
sideration is given to the whole : and after the advantages 
or disadvantages are summed up, the heat to be given to 
the gun-block is determined upon, and it is thereby brought 
to the highest conditions of strength, elasticity, ductility, 
and toughness, of which it is susceptible. Some specimens 
after tempering are found to stretch from 15 to 25 per cent, 
of their length, thus showing a degree of ductility which is 
surprising, and combining the qualities of steel and wrought 
iron in the gun-barrel. 

The next Table shows the behaviour of gun steel in the 
testing machine. 



Steel. 



75 



Breaking 
weight per 
square inch 

of section 
in tons. 


3479 


i 
i 

to 

i 


Elasticity as 
shown by the 

difference 
between the 
visible and 

permanent 
elongation. 


888 ! 


*o 

io n ui i^in 
w co co co ^i- -rr rr *o i 
OOOQOOOO 
0000000 ' 


a 
a 

il . 

bos o 

c-S.2 

.s 


c 
u 
c 
nj 

S 

PL, 


. m CON 

O O t~- 

1 pop 


INI l§88l 


3 

> 


888 1 


vo 
lO N iO lO , 
M ro ro CO Tf iovO 00 

oooooooo' ' 
pppppopp 


Length 
of 

specimen 

in 
inches. 


N 


N 


Diameter 

of 
specimen. 


co 

co 


co 

CO 


Weight 

applied in tons 

per square inch 

of section. 


O">00 O On 
fO On ^1- 1^ 
N rourt 


1 

w 00 VD i-i NO OWO 00 
O N^p p\ O N^O N 
VOONO "1"1N N COCO 


O 

rt 


Soft cast Steel in 
natural state. 


Cast Steel tem- 
pered at a high 
heat by immer- 
sion in oil. 



76 On the Strength of Materials. 

As the result of a long course of valuable experiments 
made by Mr. G. Berkley, C. E., he draws the following 
general conclusions : ' First, that Bessemer steel will bear 
before rupture a minimum tensile strain of 33 tons per 
square inch of section, and stretch about 1 inch in 12* 
inches of its length ; second, that the same material will 
bear, either in tension or in compression, a minimum stress 
of 17 tons, before the extensions or compressions per unit 
of stress become irregular or excessive, as compared with 
those which have preceded them, in other words, ' before 
the yielding point of the material is reached ; third, that 
this material will probably contain about '45 per cent, of 
carbon, chemically combined with the iron ; and, fourth, 
that this description of steel, if properly made and annealed, 
is as uniform in quality as wrought iron, and may therefore 
be employed (precautions being taken to test its quality) as 
a substitute for wrought iron, while allowing an increase of 
strain of 50 per cent, to be imposed upon it.' 

Different qualities of steel have varying ability to resist 
compression ; with ten specimens of highly converted cast 
steel, of a quality suitable for cutting instruments, an average 
of 76,000 lbs. was required to compress the specimen 
ToVo^h of an inch. With ten specimens of soft mild cast 
steel of the finest quality, the softest required 25,000 lbs., 
the hardest 46,000 lbs., or an average of 3 5, 5 00 lbs. to produce 
the same impression ; while two specimens, cut from a 
Krupp gun, required an average force of 25,300 lbs. One 
of these specimens was afterwards flattened down into a thin 
disc without cracking at the edges, thus showing a remark- 
able degree of malleability in the cold state. In all these 
experiments the specimens at the commencement were 1 inch 
in length and '533 inch in diameter. 



77 



CHAPTER VII. 

ON COPPER AND OTHER METALS, AND THEIR ALLOYS. 

Copper. 

The reddish-brown sonorous metal termed copper is pos- 
sessed of considerable strength and elasticity. It is a metal 
which is both malleable and ductile, but it possesses the 
former property in a higher degree than the latter ; hence, 
it is much better fitted to be hammered, rolled, or worked 
into thin hemispherical pans, or sheets, or other forms, than 
to be elongated into a fine wire by pulling it through a draw- 
plate. It is likewise to be noted that both properties, malle- 
ability and ductility, depend upon, and are mostly due to 
the purity of the metal. 

Next to iron, in its various conditions, copper is one of the 
most important and useful metals found in the workshop, 
and is extensively employed in the mechanical arts. Its ores 
are widely distributed, and are found more or less abundantly 
in almost every country in the world. Copper probably has 
been longer in common use than any other metal. 

As will be seen by the Tables in this chapter, its tenacity 
is somewhat uncertain, and is not at any time equal to that 
of either wrought iron or steel ; but still as it is superior in 
strength to gold, platinum, or silver, and indeed to all the 
softer metals, and possesses many of their good properties 
besides, it is held in high estimation. 

A square inch of good wrought copper will break with a 
tensile strain of about 15 tons ; but it is not so strong in the 
ingot or cast condition, for in that state it will often break 
with less than the half of the above tension. The effect of 
working upon copper is remarkable, both as regards its 
malleable and its ductile properties ; even a piece of good 



7 8 On the Strength of Materials. 

copper wire, -^th of an inch in diameter, may be worked up 
to such a condition, that it will require a strain of 300 lbs. 
to pull it asunder. 

At page 120 of Mr. Bloxam's treatise on Metals, there will 
be found much useful information respecting the quality of 
copper, as depending upon the refining or toughening pro- 
cesses of its manufacture, by which it will be seen that it 
is altered, from a brittle state, into one which is soft, malle- 
able, and ductile ; but in the hands of the unskilful founder 
or furnace manipulator, the malleable copper, from mis- 
management, may again become brittle by the absorption 
of charcoal, and, when such is the case, it has to be again 
refined by the action of air, while melted in the crucible 
of the founder. 

It may be observed that, in the working of copper, either 
by drawing, rolling, or hammering, it is altered in the same 
way as wrought iron or steel ; under the operation it be- 
comes rigid, stiff, hard, and liable to crack, or even to dis- 
integrate, and it can only be restored to its normal quality 
by a course of annealing, which may sometimes require to 
be several times repeated. This change is mechanical, and 
is quite distinct from the chemical change to brittleness 
before referred to. 

Copper, even when employed by itself, is extensively used 
for manufacturing purposes, but the articles made of pure 
copper are few in number, when compared with the mani- 
fold forms in which it appears when combined with other 
metals. It is also the hardest as well as the most tenacious 
of all the workshop metals, except iron and steel, and it 
may be worked by the smith either cold or hot. When 
heated to redness, it can be forged, drawn down, or upset 
much in the same manner as wrought iron, but when it is 
heated to fusion or even to redness", and at the same time 
exposed to the atmosphere, it is found that the exterior 
surface is rapidly converted into black scales of peroxide. 
This may be roughly removed by heating and plunging into 



Copper and other Metals, and their Alloys, 79 

cold water, or the pure metallic surface may be laid bare by 
immersion in a solution of ammonia ; but by repetition of 
the above process the copper may be entirely wasted. 

In ordinary use it is very liable to corrosion, by the mere 
exposure of the bright parts of the metal to a damp atmo- 
sphere. The green oxide of copper so produced being poi- 
sonous, it is of importance that any copper vessels used for 
culinary purposes should be kept perfectly clean ; the usual 
precaution is, to cover the interior surface of the copper with 
a coating of tin, but this does not afford perfect security, as, 
from its softness, it is liable to be scraped or otherwise worn 
off, by the tear and wear of daily use. 

Copper has been used to a considerable extent for the 
construction of steam boilers, more especially for marine 
purposes, or where salt water has to be evaporated. But, 
of late years, it has been entirely superseded by iron or 
steel. Although copper does not ordinarily rust to the same 
extent by the action of salt water, still it is more rapidly 
damaged in the furnaces by the use of sulphurous coal, and 
when the boiler does happen to leak from any cause, the 
leakage does not take up so readily as with iron, and the salt 
incrustation is found to deteriorate the metal more, in the 
vicinity of the leakage ; besides, copper is sooner reduced in 
tenacity by over-heating. Iron does not become perceptibly 
weaker up to a temperature of 570 , after that temperature 
is reached, the strength gradually decreases : whereas copper 
is in its best state when cold, and loses tenacity by every 
increase of temperature. With so many disadvantages, and 
having a tenacity of only 15 tons, it is now disused, and 
iron or steel is now almost invariably employed for steam- 
boilers, except in some special cases. 

The specific gravity of copper has a considerable range ; 
it varies from 878 in the crude state to 9-0, after rolling or 
hammering. An increase of density was supposed to arise 
from the mere condensation of the particles of the mass, but 
it is now suggested that when copper is melted in contact 



8o On the Strength of Materials. 

with the atmosphere, it absorbs oxygen, which does not 
afterwards find the means of escape, and consequently the 
metal becomes slightly porous ; this absorption of oxygen is 
in a measure prevented by careful fusion under common 
salt The density of the metal, so fused, is nearly equal to 
that of worked copper, namely 8*921, and after being sub- 
jected to a pressure of 300,000 lbs. per square inch, it in- 
creases to 8-930 ; this difference however is small, and it 
has been suggested that the change may be more owing to 
a diminution of the empty spaces still remaining, rather than 
to the approximation of the molecules. 

Articles which, from their form, require to be cast in a 
mould, are seldom made of pure copper, because it is too 
soft for the generality of purposes ; it is likewise very porous 
after casting, and has great tendency to unsoundness. Copper 
melts at 2,000°, which is higher than the melting-point of 
most of its alloys, as given in Table XVII. 

The ultimate tenacity of copper when in the cast state 
ranges from 19,000 to 26,000 lbs. per square inch of sec- 
tion; but the strength of this copper may be considerably 
increased by working, wire-drawing, hammering, or consoli- 
dating. When carefully drawn into wire, copper has a 
tenacity as high as 60,000 lbs. per square inch ; ordinary 
copper bolts a tenacity of 33,000 lbs. ; while several other 
specimens, of pure wrought copper bolts, gave an average 
ultimate tenacity of 36,000 lbs. per square inch. 

Copper, in castings, is generally mixed with other metals ; 
such mixtures of metals are called alloys, and those alloys in 
which copper predominates are the most numerous ; tin, 
zinc, lead, phosphorus, aluminium, iron, and other metals 
are all employed to form alloys with copper. 

The fluidity and tenacity of copper may both be con- 
siderably increased by the addition of a small percentage 
of phosphorus. In several experiments that were made, 
this alloy was remarkable for its density and tenacity, and 
when broken showed a regular, sound, and uniform frac- 



Copper and other Metals, and their Alloys. 8 1 

ture Mr. Abel found that by an addition of from 2 to 
4 per cent, of phosphorus, a metal was obtained more uni- 
form than bronze, and having an ultimate tenacity of from 
48,000 to 50,000 lbs. per square inch. Mr. Overman states 
that by the addition of phosphorus, copper may be rendered 
as hard as steel. The combination of phosphorus with 
copper increases the tendency to corrosion, unless another 
metal, such as tin, is also added. By adding phosphorus to 
bronze, its homogeneity is materially increased, and its ten- 
dency to oxidise by exposure to the atmosphere completely 
neutralised. 

The two following Tables show the results of experiments 
with exceptionally good copper, and with copper containing 
a small percentage of phosphorus. 

Results of experiments made at Woolwich, to ascertain 
the tensile strength of copper : — 

TABLE XI. 

Length of specimen under test, 2 inches. 



Breaking weight 

in tons per square 

inch of section. 


Specific 
gravity. 


Remarks. 


15-39 
H-78 
14-89 

1 1 79 


8-688 


Cast copper 
(very pure). 


1575 
16-25 

15-9 

16-25 




Specimens cut from virgin 
copper bolts. The bolts were 
2^, 2, 1, and | inch diameter 
respectively, and the diameter 
of the specimens cut from the 
bolts, 1", 1", -6", -6". 



The above results, especially those on cast copper, indi- 
cate a better quality of copper than the average. 

G 



82 



On the Strength of Materials. 



Results of experiments made at Woolwich to ascertain the 
tensile strength of phosphorised copper : — 

TABLE XII. 
Length of specimen under test, 2 inches. 



Breaking weight in tons 


Specific 
gravity. 


Percentage 


Diameter 


per square inch 


of 


of specimen in 


of section. 


Phosphorus. 


inches. 


6-23 





I 


113 


7'56 


8- 202 


I 


113 


16-47 


8-592 


I 


113 


I7'I3 


8-876 


*h 


113 


19-0 


— 


1 


113 


20*25 


8-614 


2 


113 


20-34 


— 


1 


113 


20-41 


8-580 


2 


•98 


21*27 


8-615 


2 


1-13 


2I*- 3 8 


8-422 


3 


112 


21-5 









The above nine specimens show an average tenacity of 
about 20 tons per square inch. The first two specimens are 
not included. 

Bronze and Gun-metal. 

The alloy of copper and tin, usually termed bronze, but 
sometimes gun-metal, has been of great value and importance 
in the arts, from time immemorial. When this alloy is used 
for artillery purposes, it generally consists of from 90 to 90 \ 
parts of copper, and from 9 J to 10 parts of tin. A small 
fraction of the tin, however, is invariably lost in the melting 
process, even if performed in crucibles, still more is lost 
when a reverberatory furnace is employed, and most of all 
if the fusion is made in a cupola. When copper and tin are 
alloyed in proper proportions, a harder metal than either is 
produced, with a density greater than the mean density of 
the constituents. The alloy is more fusible than copper, 
and less liable to corrosion. 

Copper and tin mix well in almost all proportions, a 



Copper and other Metals, and their Alloys. 83 

small percentage of the latter rendering the alloy both hard 
and tenacious, and by changing the proportions of tin to 
copper, alloys are formed, varying extremely in colour, hard- 
ness and soundness, and also in regard to their capability 
of yielding a sonorous sound when struck, as when used for 
bells. 

By the addition of tin, hardness is increased. With a 
proportion of |th of tin to f ths of copper, by weight, the metal 
assumes its maximum hardness for the purposes of the 
engineer, or for any application in which it requires turning 
or planing. The founder sometimes resorts to a mixture 
containing from Jth to -Jrd of tin, it then becomes highly brittle 
and elastic, like glass, and the sonorous property is im- 
proved in a high degree ; at the same time its brittleness 
rather than its hardness is the prominent feature. A mix- 
ture, consisting of 2 parts of copper and 1 of tin, forms an 
alloy so hard that it cannot be cut with steel tools, and 
has a highly crystalline structure. At this stage almost 
every characteristic for which tin and copper are distin- 
guished seems to be entirely changed. 

The specific gravity of ordinary bronze varies from 8-4 
to 8 '94, according to the nature of the mixture and the way 
in which it has been treated by the founder. From Mus- 
chenbroek's experiments, it appears, that the density of the 
alloy becomes greater, as the proportion of tin is increased : 
with 10 parts of copper and 1 of tin, the specific gravity was 
8*351 ; with 8 parts of copper and 1 of tin, it was 8*392; with 
6 parts of copper and 1 of tin, it was 8*707, and with 4 parts 
of copper and 1 of tin, it was 8*723. The results obtained in 
experiments made at Woolwich showed-^, rather lower specific 
gravity than the foregoing, and Major Wade states that, 
judging from an examination of the specimens obtained from 
the heads of all the guns cast at an American foundry, the 
density varied from 8*308, to 8*756, thus showing a difference 
of weight between the lightest and heaviest specimens of 
28 lbs. in the cubic foot. 

C2 



84 On the Strength of Materials. 

Bronze, melting at 1,900° Fahr., is more fusible than 
copper, but much less fusible than tin. Indeed, the differ- 
ence of fusibility in these two metals is so great, as to render 
it exceedingly difficult for the founder to obtain a perfectly 
homogeneous bronze alloy, when the casting is in great mass ; 
upon examination it is often found that specimens of large 
castings show a great want of regularity, and contain patches 
or spots of the appearance of tin, mechanically interposed 
between the particles of alloy. These spots, although ap- 
parently of tin, seldom contain more than 25 per cent, of that 
metal. 

In forming bronze, great care must be exercised by the 
founder, when mixing the metal in the furnace. The more 
refractory metal should be melted first, and the more fusible 
metal added. The alloy should be well stirred and then 
cast, and should be cooled as rapidly as possible, in order 
to obtain uniformity and compactness, and to obviate the 
tendency to separation in the process of cooling, the denser 
metal being generally found at the lower part of the casting, 
and the lighter one at the top, if the cooling is long pro- 
tracted. 

When mixing tin with copper in the furnace, it is of the 
utmost importance that the tin should not be long exposed 
to the influence of the air, because, when it is heated to 
redness, its affinity for oxygen is so great that it will be 
rapidly oxidised and converted into the peroxide or putty 
of tin (the putty-powder of commerce). This is very dis- 
advantageous, for when a reverberatory furnace works 
slowly, the metal is found to contain innumerable particles 
of the putty-powder, and to such an extent is this sometimes 
the case, as to render the turning or boring of the gun a work 
of extreme difficulty, because the cutting instruments are 
blunted by the hard oxide. Hence it is that the crucible 
system of melting has a great advantage over the large 
reverberatory furnace, wherever it is applicable, the chief 
barrier to the use of the crucible being the difference in cost. 



Copper and other Metals, a?id their Alloys. 85 

In mixing copper and tin to form gun-metal, the best 
arrangement is to alloy them first in the proportion of 2 to 
1, obtaining a white hard crystalline silvery speculum 
metal, and then by another melting to mix this hard alloy 
with the requisite quantity of copper to give the required 
quality of bronze. In this second melting, as well as in 
the first, the copper is first melted ; then, shortly before 
the time of casting, the 2 to 1 alloy is added, and the whole 
well stirred to secure a good mixing. It is afterwards im- 
mediately cast in order to prevent the oxidation of the tin. 

A small quantity of zinc is sometimes added to common 
bronze, for the purpose of making it mix better. Zinc in- 
creases the malleability without materially reducing the 
hardness, but it is seldom used in gun-metal. 

The investigation bestowed upon the strength and other 
properties of bronze, during the last hundred years, has been 
most thorough • many experiments have been made, but the 
results are so discordant as to render it difficult to give an 
account of them -without inserting such a number of tables 
as would be incompatible with the size of this volume. 

The late Mr. Rennie came to the conclusion, that the 
average ultimate tenacity of gun-metal is about 36,333 lbs. 
per square inch, that is, when the mixture consists of copper 
and tin only, and in the usual proportions. Muschen- 
broeck's experiments go to show that with a mixture of 6 
parts of copper and 1 part of tin, the ultimate tenacity is 
equal to 44,000 lbs. per square inch. From similar experi- 
ments made at Woolwich, the following results were ob- 
tained, with a mixture of — 

Tenacity. 
12 parts of copper and 1 of tin, 29,000 lbs. per sq. inch. 
11 „ „ 3°>70o ,, 

10 ,, „ 33>°°° ,, 

9 „ „ 38,000 ,, 

The above results are not quite uniform, but they nearly 
agree with those obtained both by Rennie and Muschen- 



86 On the Strength of Materials. 

Droeck, and are perhaps not far from the average of the 
bronze usually met with in the arts. 

Judging from an immense number of experiments made 
at Woolwich, at different times, during the past fifteen years, 
and without having regard to many minor points, or to the 
shades of proportion of mixtures and different modes of 
casting, the average tenacity of bronze is 31,280 lbs., 
varying from 22,500 lbs. to 41,000 lbs. per square inch. 
As a rule, it begins to yield visibly, and to take permanent 
set at 15,164 lbs., and the average ultimate elongation per 
inch in length is '290 of an inch. 

Some experiments are recorded, both much lower and 
much higher than the above, even ranging from 17,698 lbs. 
upwards to 56,786 lbs., but these are exceptional, and 
33,000 lbs., which is between 14 and 15 tons, maybe con- 
sidered as the general average of good bronze. 

Major Wade, of the United States Army, has given great 
attention to this point, and he has found the ultimate 
tenacity to vary from 23,929^35. to 35,484 lbs. per square 
inch, a difference in the ratio of 2 to 3. These differences 
occurred in samples taken from the same part of different 
castings of gun-heads, where the materials used were appa- 
rently all of the same quality, and were melted, cast and 
cooled in the same manner, and every effort was used to 
have them similarly treated in all respects ; but the causes 
of such irregular and unequal results, when the materials 
used and the treatment of them were apparently the same, 
are very obscure and perplexing. 

Benton states that the quality of bronze depends much 
upon the nature of the furnace treatment of the melted metal, 
and that by extreme care, and by this alone, the tenacity 
of bronze made at Washington Navy Yard Foundry has been 
raised as high as 60,000 lbs. per square inch, so as to equal 
in tenacity good wrought iron, which is worth noting. 

The following results have been obtained by analysing a 
number of tables which show the tensile strength of various 



Copper and other Metals, and their Alloys. 87 

specimens taken from different parts of bronze guns, some 
. of the specimens being cast in open moulds with both green 
sand and dry sand ; others in closed moulds with green sand, 
and the remainder in iron moulds, forming large chills to 
cool the metal rapidly. 

The average weight in lbs. per square inch, required to 
overcome the elasticity of the metal was 14,694 lbs., and 
the point of fracture 27,305 lbs. per square inch, the average 
elongation per inch in length being -144 inch. Each speci- 
men was ro66 inch in diameter, and the length of breaking 
part 2 inches. 

In sixteen specimens, each "533 of an inch in diameter by 1 
inch in length, the compressive stress per square inch required 
to produce a permanent set of *ooi ranged from 5*4 tons 
to 7 tons, and was usually near to a mean between these 
two extremes. A stress of 7 tons applied to each specimen 
produced a permanent set ranging from "0015 to "0005, the 
most elastic having been cast in an iron mould which cooled 
the metal rapidly. Taken as a whole, the bronze when in 
compression, showed a permanent set of '00 1 of an inch with 
an average compressive load of 13,843 lbs. per square inch, 
and '384 with 50 tons per square inch, with which load the 
specimens were fractured. When compared with steel, or 
even iron, bronze offers a small resistance to compression ; 
but its compressibility is found to depend greatly upon the 
perfection of the alloy, and the amount of fluid pressure 
induced by the height of the deadhead, and the rate of 
cooling employed to prevent the separation of the tin. 

Brass. 

Of the many useful alloys known to the mechanical world, 
brass is perhaps the one which is most extensively used, 
being easily worked, and of a fine yellow colour. In this 
alloy as in nearly all the others used in construction, copper 
is the most prominent metal. 



38 On the Strength of Materials. 

In the melting and mixing of copper and zinc, great care 
has to be exercised to prevent the zinc from passing away in 
vapour, which is usually effected by covering the crucibles 
with charcoal powder and a close lid of clay. Brass is more 
malleable than copper when in the cold state, but it will 
not submit to be forged at a red heat, on account of the 
low melting point of zinc ; even a small addition of zinc to 
copper will affect it in this important respect, which is a 
disadvantage. 

Tin and lead are sometimes added to copper and zinc m 
making brass. The quantity of copper varies from 60 to 92 
per cent, and it is not uncommon to add from ^ to 3 per 
cent, of lead, and from J to 3 per cent, of tin, according to the 
nature of the work for which the alloy is required. The best 
proportion for fine or yellow brass appears to be copper 
2 parts and zinc 1 part. 

The specific gravity of brass ranges from 7*82 to 8*5, and 
is thus greater than the mean of its constituents, that of cop- 
per being 878 and of zinc 6*86, which is probably due to the 
zinc finding empty spaces, into which it enters. 

The melting point of brass is lower than the mean of its 
constituents would indicate, being from 1689 Fahr. to 1900 
Fahr., the fusibility entirely depending upon the quantity of 
zinc which has entered into combination with the copper ; 
and the fact of the fusibility of the alloy increasing with the 
further addition of zinc furnishes strong evidence that the 
change in their properties, which the metals undergo, arises 
from chemical affinity. The liquidity of this alloy may be 
very much increased by adding a small portion, say half an 
ounce, of dry phosphorus in the crucible, and then stirring 
the metal before running it into the mould ; by this means 
the alloy is rendered so liquid that very thin and sound cast- 
ings may be obtained without difficulty. 

The addition of a little lead causes brass to be more duc- 
tile and better adapted for turning in a lathe than common 
brass, while a large addition of lead renders it very brittle, 



Copper and other Metals, and their A Hoys. 89 



and if the proportion of lead amounts to nearly one half, 
then a partial separation takes place in the act of cooling. 
The tenacity of fine brass (as stated by Rennie) is only 
about 18,000 lbs. per square inch ; but the average ultimate 
tenacity of the best quality of brass, when composed of two 
parts copper and one part zinc, is much higher, being 
28,900 lbs. per square inch. 

Muntz-metaL 

The alloy of 60 parts copper and 40 parts zinc, termed 
' Muntz-metal,' is a mixture which has been much used for 
the sheathing of ships, and for the bolts of marine engines 
liable to rust, and for similar purposes. Its tenacity is 
about 22 tons per square inch, or nearly equal to that of 
good wrought iron, while its endurance in salt water is 
nearly equal to that of bronze or brass. 

In consequence of the high tenacity of this metal, it was 
thought desirable to cast guns of it, but it was found that, 
during the increase of temperature due to rapid firing, the 
presence of zinc affected the tenacity of the metal to a 
considerably greater extent than is the case with ordinary 
gun-metal, and, notwithstanding its great strength, it was 
found unsuitable. 

The following Table shows the results of various experi- 
ments made at Woolwich to ascertain the tensile strength of 
brass, &c. : — 

TABLE XIII. 
Length of specimen under test, 2 inches. 



Breaking weight 

in tons per square 

inch of section. 


c~^„:fl~ Diameter 


Mixture. 


16-02 
16-02 

I3-35 
IO-57 

io-68 

10-91 

3-12 

3 -22 


8-58 h 

8-534 
8-699 

7-049 
6-915 


- 113 

J -3 


1 Copper, 7 lbs. , 

j zinc, 3 lbs. 8 ozs. 

]_ Copper 10 parts, iron 
) IO parts, zinc 80 parts. 



90 On the Strength of Materials. 

The average ultimate tenacity of the first 6 specimens 
was 12-92 tons or 28,940 lbs. per square inch. The result 
of the last two experiments is instructive. 

Sterro-metal. 

' Sterro-metal ' is a new alloy of copper, zinc, tin, and 
wrought or pure iron. One of the principal objects for 
which this particular kind of metal was first introduced 
was, to supersede the use of cast and wrought iron, and 
bronze, in the manufacture of heavy ordnance. Cast iron 
is objectionable on account of its low tenacity, elasticity 
and ductility, and has proved not altogether suitable for the 
purpose. Wrought iron is rather too soft for the interior 
of guns ; necessitates, in its manufacture into guns, a great 
amount of expensive working, and, even when the greatest 
care and skill is exercised, its perfect soundness cannot be 
altogether depended upon. Bronze, wmen of the proper 
quality, is too soft ; its ultimate tenacity is uncertain, being 
generally not much greater than that of good cast iron ; it 
is more easily stretched to the elastic limit than is the case 
with good wrought iron ; and, in addition to all these ob- 
jections, it is more costly. 

For the foregoing, as well as for other reasons, many 
efforts have been made to obtain a homogeneous and dense 
metal, which could be cast into large masses, and which 
combines all the good properties of hardness, great tenacity, 
elasticity, and soundness. 

Sterro, or firm metal, was first introduced to the arts in 
Vienna, a few years ago, by Baron de Rosthorn, and was 
rapidly seized hold of by experimentalists in various parts of 
the world. At Woolwich a series of interesting experiments 
were made, with specimens containing different proportions 
of the various metals, prepared in the Royal gun factories, 
as well as with specimens of the metal obtained from Austria. 
Since that time additional experiments have been made, 
and the results are given in the following Tables. 



Copper and other Metals, aiid their Alloys. 91 

From these it will be seen that this alloy has some most 
valuable properties, especially stiffness, as its name implies, 
together with great tenacity and power of resisting compres- 
sion, with considerable hardness, which is very desirable in 
any gun-metal, to resist the abrasive effect of the projectile. 
Although the sterro-metal possesses the most prominent 
of these qualities in a high degree, yet, even with this metal, 
it is very difficult to ensure a perfectly uniform and sound 
casting with any degree of certainty, several fractured speci- 
mens showing the mixture of metals to have been very 
incomplete. 

From the following Tables it will be seen that the ultimate 
tenacity varies from 43,000 lbs. to 85,000 lbs. per square 
inch, or an average of 60,480 lbs. per square inch ; it also 
required a strain of 30,000 lbs. to produce a permanent 
elongation of '002 of an inch per inch of length, while the 
ultimate elongation with the average strain of about 60,480 
lbs. per square inch was "0675 of an inch per inch of length. 
Whereas, bronze begins to yield at 15,000 lbs., and is frac- 
tured at 33,000 lbs. per square inch, and shows an ultimate 
elongation of "290 of an inch per inch of length. 

The recent experiments made with steel, and especially 
with steel tempered in oil, and the practical success which 
has attended it for gun purposes, has probably barred the way 
to further experiments being made with sterro-metal, at least 
for the present; but it will be evident that the subject opens 
up a wide field for other experiments with mixtures of iron 
and other metals, with a view to discover other combinations 
which will give strength with other good qualities. 

Results of experiments made at Woolwich to ascertain the 
tensile strength of sterro-metal : — 



9 2 



On the Strength of Materials. 



TABLE XIV. 

Diameter of specimen, 707 inch ; length of part of specimen 
under test, 2 inches. 



1 


Strain at 








Breaking 


permanent! 


Ultimate 






weight in 


elongation j 


elongation 






tons per j 


of '002 in. 


it breaking 


•Treatment. 


Mixture. 


square inch 


per inch 


point in 






of section, j 


of length 
in tons. 


inches. 






2675 ! 


6-75 


I 


as received. 


Austrian. 


21-5 


ii-o 


•05 


j cast in sand. 


Copper 60, zinc 39, 
iron 3, tin 1 -5. 


19-25 


13-75 


•OI5 


J 


^ 


24-25 


17-25 


•Ol6 


cast in iron. 
\ cast in iron and 


(.Copper 60, zinc 44, 


23^5 


15-25 


•02 


/ annealed. 


F iron 4, tin 2. 


28-0 


17-0 


•045 


forged red hot. 


J 


3I-6I 


— 


— 


( cast in iron and 


— — 


32-52 


— 


— 


\ forged red hot. 


— — 


34'0 


— 


— 


— 


Copper 60, zinc 37, 
iron 2, tin 1. 


3 8-0 


— 


— 


— 


Copper 60, zinc 35, 
iron 3, tin 2. 


27-0 


— 


— 


after simple 
fusion. 


Copper 55 -04, spelter 


34 -o 


— 


— 


forged red hot. 


\ 42-36, iron 1-77, 
J tin -83. 


380 


— 


— 


drawn cold. 


280 


— 


— 


after simple 
fusion. 


| 


32-0 




I 


forged red hot. 
drawn cold and 
reduced from 


i Copper 57-63, spelter 
" 40*22, iron 1*86, 
tin 0-15. 


37 'o 


— 


j 


100 to 77 trans- 






i 


verse sectional 








\ 


area. 





The next Table shows the results, of experiments made at 
Woolwich to ascertain the extension and tenacity of sterro- 
metal : — 



Copper and other Metals, and their Alloys. 93 



TABLE XV. 

Diameter of specimen, 707 inch ; length of part under test, 2 inches. 



I 


2 


3 


4 


5 


6 


Breaking 

weight in 

tons per 

square inch 

of section. 


Weights 
applied in 
tons per 
square inch 
of section. 


Elongations in 
decimals of an 
inch due to the 
weights applied 
in column 2. 


Permanent 
elongations in 
decimals of an 
inch due to the 
weights applied 
in column 2. 


Permanent 
elongations 
per inch of ' 

length in 1 
decimals of 

an inch. 


["reat- 
nent. 




2-27 


•OOI 










3-86 


•002 










6-02 


•OO3 










7-27 


•OO4 










8-98 


•005 


•001 


•OOO5 






10-40 


•006 


'001 5 


•00075 






1 1 03 


•007 


•002 


•001 






12-50 


•008 


•0035 


•OOI75 






13-07 


•009 


•004 


•002 




20-35 




•074 










4-09 


•001 








5-68 


•002 










6-48 


•OO3 


•0005 


•OOO25 






6-93 


•OO4 


•001 


•OOO5 






773 


•OO5 


•0025 


•OOI25 






8-30 


•006 


•003 


'OOI 5 


V, 




9-21 


•008 , 


•005 


•OO25 


9 


1978 




•227 






Via 

u 




5" 


•002 








7-16 


•OO4 


•001 


•OO5 




8-07 


•OO5 


•0025 


•OOI25 






8-41 


•O06 


•003 


'001 5 






875 


•OO7 


•004 


•002 






9-32 


•OO9 


•0055 


•00275 




20-92 




•282 










4'54 


•002 


'O005 


•0025 




6-36 


•OO4 


•001 


•0005 






IO-I2 


•O06 


•0025 


•00125 




19-21 


I2-50 


•OO9 


•0045 


•00225 






7'50 


•OO3 


•0005 


•0025 




n-37 


•OO5 


•001 


•0005 






13-19 


•OO7 


•002 


•001 




20-35 


14-66 


•OO9 


•004 


•002 





94 



On the Strength of Materials. 



Table XV '.— continued. 



I 


2 


3 


4 


5 : 6 


Breaking 
weight in 
tons per 
square inch 
of section. 


Weights 
applied in 

tons per 
square inch 
of section. 


Elongations in 
decimals of an 
inch due to the 
weights applied 
in column 2. 


Permanent 
elongations in 
decimals of an 
inch due to the 
weights applied 
in column 2. 


1 
Permanent 
elongations Treat- 
per inch of ment. 

length in 
decimals of j 

an inch. 




5-23 


•002 










8-64 


•004 




^_ 




I4-IO 


•006 


•OOO5 


•OOO25 






I5H6 


•007 


•001 


•OOO5 







I7-05 


•008 


•OO25 


•OOI25 






18-53 


•OI 


•OO3 


•OOI5 


UJ 


32-52 






•167 


•0S35 


j 




































5-57 


•O02 








9-66 


•OO4 










13-75 


•006 


•001 


•0005 




16-26 


•008 


•0025 


•OOI25 


rt 




16-94 


•OI 


•0035 


•OOI75 


u 


30'02 






•167 


•0835 


/ 














4-32 


•OOI 










6-25 


•002 










8-07 


•003 






^ 




9-21 


•004 






'a? 
> 




10-23 


•0055 


•0015 


•OOO75 







10-91 


•O065 


•0025 


;ooi25 


<£ 




11-14 


•007 


•003 


•0015 


tJ 




11-82 


•008 


•0045 


•00225 






12-28 


•OI 


•005 


•0025 


■1 




20-35 




•132 
















& 1 












■£, 




5-23 


•001 






2 




8-52 


•OO3 






c 




10-57 


•OO5 


•001 


•0005 






11-14 


•O06 


•002 


•001 


in 




12-05 


•008 


.0045 


•00225 


O 




12-50 


•01 


•005 


•0025 




21-26 




•156 









Copper and other Metals, and their Alloys. 



Table XV. — continued. 



I 


2 


3 


4 


5 


6 


Breaking 
weight in 


Weights 
applied in 


Elongations in 
decimals of an 


Permanent 
elongations in 
decimals of an 


Permanent 
elongations 
per inch of j 


Treat- 


tons per 
square inch 
of section. 


tons per 
square inch 
of section. 


inch due to the 

weights applied 

in column 2. 


' inch due to the 

weights applied 

in column 2. 


length in 

decimals of 

an inch. 


ment. 




4-20 


•OOI 






) 




6-02 


•002 










8-52 


•003 










10-34 


•OO4 










1273 


•OO5 










14-32 


•O06 


•OOO5 


•OOO25 






14-78 


•007 


•001 


•OOO5 






17-28 


■009 


•OO25 


•OOI25 




27-06 


18-76 


•OI2 


•OO45 


•OO225 







6-36 


•002 








9-21 


•OO4 


•OOO5 


•OOO25 


! 




10-57 


•006 


•OO25 


•OOI25 




11-82 


•009 


•OO45 


•OO225 


24-56 






•275 


•1375 


U 

! 




7-84 


•003 








9 '55 


•OO4 










13-19 


•005 


•OOO5 


•OOO25 






14-78 


•O06 


•OOO5 


•OOO25 






i5'46 


•007 


■001 


•OOO5 






I7-39 


•008 


•0025 


•OOI25 






18-53 


•OIO5 


•0035 


•OOI75 




25-69 






•037 


•0185 


J 
\ IP 

to 




3-52 


■002 




- 




6-82 


•004 






,0 




10-91 


•006 










1228 


■007 










i;*92 


■008 


•0005 


•OOO25 


1 




16-37 


•009 


'0007 


•OOO35 




17-28 


•OI 


■001 


•OOO5 


a 




I9-33 


•OI2 


•0025 


•OOI25 




5h 




21-83 


•OI55 


•005 


•OO25 


G 


32-29 






•12 


•06 , 


to 




1 




I 


i U 



9 6 



On the Stre?igth of Metals. 
Table XV. — continued. 



I 


2 


3 


4 


5 


6 


Breaking 
weight in 

tons per 
square inch 
of section. 


Weights 
applied in 

tons per 
square inch 
of section. 


Elongations in 

decimals of an 

inch due to the 

weights applied 

in column 2. 


Permanent 
elongations in 
decimals of an 
inch due to the 
weights applied 
in column 2. 


Permanent 
elongations 
per inch of 
length in 
decimals of 
an inch. 


Treat- 
ment. 




3-i8 

5-68 


•002 
•OO4 






t/3 




8-87 


•O06 










978 


•007 






0> 




12-05 


•008 


•OOO5 


•OOO25 


^ 




12-50 


•OO9 


•OOO7 


•OOO35 


/a 




13-30 


•OI 


•OOI 


•OOO5 


I 




15-01 


•OI2 


•OO25 


•OOI25 






17-05 


•OI55 


•OO45 


•00225 




27-5I 






•II 


•055 


in 

J V 



Results of experiments made at Woolwich to ascertain the 
transverse strength of mixtures of wrought iron and gun- 
metal : — 

TABLE XVI. 



Size of Specimen. 


Distance 
between 


Deflection 

in 

inches. 


Breaking 

v/eight 

in tons 

at centre 

of beam. 


Mixture. 


Length 

in 

feet. 


Breadth 

in 
inches. 


Depth 

in 
inches. 


supports 

in 
inches. 


2 
2 
2 
2 
2 
2 
2 
2 
2 


1-99 
2-03 

1 '99 
2-03 

2-02 
2'02 
2-04 
2*01 

2-OI 


2 

2 

2 

2-05 

2-02 

2-05 

2-03 

2-06 

2-05 


20 
20 
20 
20 
20 
20 
20 
20 
20 


•142 
•115 

•no 
•no 
•105 

•140 

•133 
•120 


2-8 

274 
2'24 
2-56 
2l6 
I - 3 I 

3-0 

2-83 

211 


| equal pro- 
j portions. 

| gun-metal 1, 
j iron 3. 

| gun-metal 1, 
j iron 7. 



It is right to state that the fracture showed the mixture of 
the two metals to be very incomplete ; nevertheless, the 
result is worth noting, as it is probably the only Table of the 
kind. 



Copper and other Metals, and their Alloys. 97 



Aluminium Brofize. 

Aluminium Bronze is an alloy of copper with aluminium, 
which seems to promise great results- It consists usually 
of 90 parts of copper to 10 of aluminium, these propor- 
tions give an alloy which may be forged either cold or hot, 
in the same manner as wrought iron, but which does not 
weld. It is highly malleable and ductile, possessed of great 
stiffness and elasticity, its specific gravity being nearly the 
same as that of wrought iron ; and it does not readily 
tarnish by exposure to the atmosphere. 

From a number of experiments made at Woolwich, its 
average tenacity was found to be 73,185 lbs. per square 
inch, and its maximum tenacity 96,320 lbs., thus its strength 
was more than double that of bronze, greater than that 
of wrought iron, or even of many of the mild qualities 
of cast steel, and at the same time its resistance to com- 
pression exceeded that of ordinary cast iron. Colonel 
Strange, who has given much attention to this alloy, states 
that its rigidity is three times that of bronze, and many 
times greater than that of brass, and that it is less affected 
by changes of temperature than either of those alloys. In 
the liquid state, it can be cast into any form without diffi- 
culty, it works nicely under the file or in a lathe, and its 
other advantages are numerous. 

In making this alloy, extremely pure copper has to be 
used, as with impure copper the alloy is much deteriorated 
in all its good properties; and to produce the best results, 
it requires to be remelted several times; the fact of remelting 
being required, in order to develope its greatest strength 
and stiffness, is not peculiar to this alloy, but is the case 
with cast iron and some of the other alloys. 

The chief barrier to the extensive use of aluminium 
bronze is the cost of the aluminium, which makes the price 
of the bronze at least four times that of ordinary gun-metal. 

H 



98 On the Strength of Materials. 

Hence this metal is chiefly used for purposes where strength 
and stiffness, combined with lightness and non-liability to 
rust, aret he chief objects, as for surveying instruments, which 
have to be light and strong, and not liable to injury when 
carried from place to place, and used in tropical climates. 

Other Alloys. 

Bells are usually made of copper and tin of various mix- 
tures, but generally in about the same proportions as for 
gun-metal. The smaller class of bells have a greater pro- 
portion of tin, to give hardness, and sometimes a little zinc ; 
even silver is occasionally added, in order to improve the 
tone. 

For such purposes, the question of strength is unim- 
portant. The same remark applies to the usual bronze 
for statues, which is a similar mixture to gun-metal, but 
analysis of different statues shows considerable variation in 
the proportions of the two metals. The addition of a small 
portion of phosphorus would have the effect of preserving 
the surface of the metal from the influence of the atmosphere, 
which fact should be noted. 

Babbitt's metal for machinery bearings, which consists of 
about 4 parts of copper and 8 lbs. of regulus of antimony 
and 96 lbs. of tin, is not a strong alloy, but it is one of 
the best reducers of friction, and its want of stiffness has to 
be provided for in the iron casing in which it is contained 
when in use, to form a bearing for a moving spindle. The 
casing is required in order to prevent it from spreading out- 
wards under the pressure to which it is exposed. In the 
use of Babbitt's metal for bearings, it is necessary to exer- 
cise great care to prevent the heating of the journal. If 
this takes place, the Babbitt's metal melts and runs out. 



Copper and other Metals y and their Alloys. 99 

Table showing the average melting point of most of the 
metals and alloys referred to in this chapter. 



TABLE XVII. 



I 

Metals and Alloys. 


Melting point 
in degrees 
Fahrenheit. 


Cast iron, rich in carbon ..... 


2786 


, , i\ to 3 per cent, of carbon 




2600 


Wrought iron ..... 




3280 


,, freed from silicon 




3500 


Cast steel, mild, -28 per cent, of carbon 




330O 


,, ordinary, -56 per cent, of carbon ,. 


3000 


,, high, 75 to *8 per cent 


of carbon 


2850 


Copper 






•• 


! 
200O 


Tin . . . . . 








442 


Zinc .... 








758 


Gun-metal . 








I900 


Brass . 








1847 


Lead .... 








6OO 


Antimony 








800 


Bismuth 








483 


Silver .... 








1873 


Platinum 








3280 


Gold .... 








20l6 



i6o 



On the Strength of Materials. 
ADDITIONAL EXPERIMENTS. 



The following Tables show the result of certain experiments on the 
resistance of metals. 





Resistance 


of Metals 


to Tension 








Size of specimen. 
I 


Nature of 
material. 


Stress in 
square 


tons per 
inch at 


Elongation 




3 
< 


Yielding. 


Breaking. 


per inch. 


per cent. 


Diameter. -533" 
area -223 sq. in. 

Length of break- 
ing part 2 inches 


Homogeneous 
steel, soft, 

Do, tempered 
in oil at a 
low heat, 

Do. tempered 
in oil at a 
high heat, 


I 297 

!> 29-9 


31-9 

47 '9 
48-5 


•123 

•129 

•08 


12-3 

I2'9 

8 


6 

g 

IS 
.5 

1 

O 
'J 

"o 

.1 


Diameter 754" 
area "4465 sq. 
inch . 

Length of break- 
ing part 2 inches 


Best gun-iron, 
soft, 


} «■* 


22'2 


•134 


i3'4 


Bronze 


6-9 


15-7 


•162 


16-2 


Copper 


— 


I5'5 


— 


"" 



Resistaitce of Metals to Compression. 



Size of specimen. 


Nature of 
material. 


Yielding 

strain in tons 

per square 

inch. 


Total compression 

with load of 50 tons 

allowed to remain on 

for 5 minutes 


Au- 
thority. 




per inch. 


per cent. 


Diameter -533" 
i Length . .1" 


Soft steel . 
Tempered steel 
Wrought iron, 

soft . 
Bronze 
Cast iron 


12-47 
28-98 

> 12-2 

• 7'5 
15*9 


•218 
•054 
•274 

•3423 
•0308 


21-8 
5'4 

27-4 

34-23 
3-08 


.5 

£.5 
•r a 




IOT. 



CHAPTER VIII. 

TIMBER. 

Although it is of less importance to investigate the strength 
of timber at the present time than it was formerly, in con- 
sequence of the diminished use of that material in per- 
manent structures, and the more general employment of 
iron, still it will always be a very valuable material for cer- 
tain purposes, and ought not to be neglected. Timber is 
variously used, even now, in permanent works, and is 
applied much more extensively in temporary structures — 
such as centerings and scaffolding. Hence its properties 
are well worthy of careful attention ; and the student should 
be familiar not only with the external appearance of the 
principal kinds of wood, but also with their relative strength, 
stiffness, toughness, and durability. 

One of the most obvious inferences to be drawn from the 
experiments recorded in the previous chapters is that very 
wide variations exist in the strength and other elastic pro- 
perties of different metals, and even of different specimens 
of the same metal. If we could investigate the properties 
of timber with the same care which has been bestowed on 
the metals, we should find that there is an even greater 
variation in the properties of different kinds of wood. This 
arises in part from the fact that timber is much affected by 
a number of external and internal conditions, during its 
growth and seasoning, and in its subsequent treatment, 
which gradually modify and change its properties. 

It will only be necessary in this chapter, to treat of the 
powers of resistance of a few among the many kinds of 
wood now employed in the mechanical arts. The greater 
number of the varieties of wood owe their commercial value 



102 On the Strength of Materials. 

to special characteristics, such as beauty of grain and capa- 
bility of being polished — the description of which does not 
fall within the scope of the present treatise. 

As a general rule, we may judge of the hardness of a 
wood by its specific gravity, if it is in its natural state. But 
the density may be increased by artificial compression (as 
in the manufacture of trenails) and this increase of density 
is generally accompanied by increase of strength. Some 
varieties of wood, as, for instance, lignum vita, are so dense 
that they sink in water, while some of the softer woods have 
not half the density of that fluid. The presence of gum or 
resin in any wood adds both to its strength and durability. 
Many woods will last a long time, if kept constantly under 
water, but scarcely any wood is very durable when allowed 
to become wet and dry alternately. 

The strength of a piece of timber depends upon the part 
of the tree from which it is taken. Up to a certain age, the 
heart of the tree is the best ; after that period, it begins to 
fail gradually. The worst part of a tree is the sap-wood, 
which is next the bark. It is softer than the other parts of 
the wood, and is liable to premature decay. The deleterious 
component of the sap-wood is absorbed, if the tree is allowed 
to grow for a longer period, and in time the old sap-wood 
becomes proper timber fibre similar to heart-wood. Hence, 
the goodness of a tree, for timber purposes, depends on the 
age at which the tree was cut down. When young, the heart- 
wood is the best ; at maturity, with the exception of the sap- 
wood, the trunk is equally good throughout ; and when the 
tree is allowed to grow too long, the heart-wood is the first 
to show symptoms of weakness, and deteriorates gradually. 

The best timber is secured by felling the tree at the age 
of maturity, which depends on its nature as well as on the 
soil and climate. The ash, beech, elm, and fir are generally 
considered at their best when of 70 or 80 years' growth, 
and the oak is seldom at its best in less time than 100 
years, but much depends on surrounding circumstances. 



Timber. 103 

As a rule, trees should not be cut before arriving at maturity, 
because there is then too much sap-wood, and the durability 
of the timber is much inferior to that of trees felled after 
they have arrived at their full development. 

The strength of many woods is nearly doubled by the 
process of seasoning, hence it is very thriftless to use timber 
in a green state, as it is not only weak, but is exposed to 
continual change of bulk, form, and stability. After timber 
is cut, and before it is properly seasoned, the outside is 
found to crack, and to split more than the inside of the 
mass, because it is more exposed to the dessicating effect of 
the surrounding atmosphere, but as the outside dries, the 
air gradually finds its way to the interior. If timber is cut 
up by the saw when green and allowed to season or dry 
in a gradual manner, it is found to be the most durable. 
In the arts, however, artificial drying is often resorted to, 
as in the case of gun stocks. These are put into a dessi- 
cating chamber, where a current of air at 90 or ioo° is 
passed over them, at such a rate as to change the whole 
volume of air in the chamber every three minutes, and it is 
found that a year of seasoning may thus be saved. The 
walnut wood is as good after this process, as if the seasoning 
had been accomplished by time and exposure, and works 
more smoothly under the cutting instruments of the stock 
machinery. 

Wood will always warp after a fresh surface has been ex- 
posed, and will likewise change its form by the presence of 
any moisture, either from that contained in the atmosphere 
or from wetting the surface. The effect of moisture on dry 
wood is to cause the tubular fibres to swell, hence it is that 
if a plank or board is wetted upon one side, the fibres there 
will be distended, and the plank in consequence must bend. 

The natural law that governs the shrinking or contraction 
of timber is most important to practical men, but it is too 
often overlooked. 

The amount of the shrinkage of timber in length, when 



104 n ti ie Strength of Materials. 

seasoning, is so inconsiderable that it may in practice be 
disregarded. But the shrinkage in transverse directions is 
much greater, and presents some peculiarities which can 
only be explained by examining the structure of the wood, 
as resulting from its mode of growth. An examination of 
the end section of any exogenous tree, such as the beech or 
oak, will show the general arrangement of its structure. It 
consists of a mass of longitudinal fibrous tubes, arranged in 
irregular circles, which are bound together by means of 
radial plates or rays, which have been variously named ; 
they are the ' silver grain ' of the carpenter, or the ' medul- 
lary rays ' of the botanist, and are in reality the same in their 
nature as the pith. The radial direction of these plates or rays, 
and the longitudinal disposition of the woody fibre, must 
be considered, in order to understand the action of seasoning. 
For the lateral contraction or collapsing of the longitudinal 
fibrous or tubular part of the structure cannot take place 
without first tearing the medullary rays, hence the shrinking 
of the woody bundles finds relief by splitting the timber in 
radial lines from the centre parallel with the medullary rays, 
thereby enabling the tree to maintain its full diameter. If 
the entire mass of tubular fibre composing the tree were to 
contract bodily, then the medullary rays would, of necessity 
have to be crushed in the radial direction to enable it to 
take place, and the timber would thus be as much injured 
in proportion as would be the case in crushing the "wood in 
a longitudinal direction. 

If an oak or beech tree is cut into four quarters, by passing 
the saw twice through the centre at right angles, before the 
splitting and contracting has commenced, the lines a c and 
b cm Fig. 10 would be "of the same length, and at right 
angles to each other, or, in the technical language of the 
workshop, they would be square, but after being stored in a 
dry place, say for a year, a great change will be found to 
have taken place, both in the form and in some of the 
dimensions. The lines ac and be will still be of the same 



Timber. 



10: 



length as before, but from a to b the wood will have con- 
tracted very considerably, and the two lines a c and b c will 
not be at right angles to each other, the angle being dimi- 
nished, by the portion shown in black in Fig. 10. The 




medullary rays are thus brought closer by the collapsing of 
the vertical fibres. 

But, supposing that six parallel saw cuts are passed 
through the tree, so as to form it into seven planks, what 
will be the behaviour of the several planks ? Consider the 
centre plank first. After due seasoning and contracting, it 
will be found that the middle of the board still retains the 
original thickness, from the resistance of the medullary 
rays, while the thickness will be gradually reduced towards 
the edges for want of support, and the entire breadth of 
the plank will be the same as it was at first, for the fore- 
going reasons, and as shown in Fig. n. Then, taking the 
planks at each edge of the centre, by the same law their 
change and behaviour will be quite different ; they will still 
retain their original thickness at the centre, but will be a 
little reduced on each edge throughout, but the side next to 
the heart of the tree will be pulled round or bent convex, 
while the outside will be the reverse, or hollow, and the 



io6 



On the Strength of Materials. 



plank will be considerably narrower throughout its entire 
length, more especially on the surface of the hollow side. 
Selecting the next two planks, they will be found to have 



Fig. ii. 




lost none of their thickness at the centre, and very little of 
their thickness at the edges, but very much of their breadth 
as planks, and will be curved round on the heart side and 
made hollow on the outside. Supposing some of these planks 
to be cut up into square prisms when in the green state, 
he shape that these prisms will assume after a period of 
easoning will entirely depend on the part of the tree to 
\rhich they belonged, the greatest alteration would be 



Fig. 12. 



Fig. 13. 




perpendicular to the medullary rays. Thus, if the square 
was originally near the outside, as seen in Fig. 12, then the 



Timber. 



107 



effect will be as shown in Fig. 13, namely, contraction in 
the direction from a to b. After a year or two the square end 
of the prism will become rhomboidal, the distance between 
c and d being nearly the same as at first, but the other two 
edges brought closer together by the amount of their contrac- 
tion. By understanding this natural law, it is comparatively 
easy to predict the future behaviour of a board or plank by 
carefully examining the end wood, in order to ascertain the 
part of the log from which it has been cut, as the angle of 
the ring growths and the medullary rays will show this, as 
in Figs. 14 and 15. If a plank has the appearance of the 

Fig. 14. 




former, it must have been cut from the outside, and for 
many years it will gradually shrink in the breadth ; while 
the next plank, shown in Fig. 15, must have been derived 
from near the centre or heart of the tree, and it will not 
shrink in the breadth but in thickness, with the full dimen- 
sion in the middle, but tapering to the edges. 

The foregoing remarks apply more especially to the 
stronger exogenous woods, such as beech, oak, and the 
stronger home firs. The softer woods, such as yellow 
Canadian pine, are governed by the same law; but, in 
virtue of their softness, another law comes into force, which 
to some degree affects their behaviour, as the contracting 
power of the tubular wood has sufficient strength to crush 



108 On the Strength of Materials. 

the softer medullary rays to some extent, and hence the 
primary law is so far modified. But even with the softer 
woods, such as are commonly used in the construction of 
houses, if the law is carefully observed, the greater part of 
the evils of shrinking would be obviated. Hence also, it is, 
that when a round block, as a mast, is formed out of a tree, 
it retains its roundness because it contracts uniformly or 
nearly so, whereas if a round spar is formed out of a 
quartering of the same tree it will become an oval, or other- 
wise contorted towards that shape. 

It would not be in accordance with the object of this 
book to enumerate all the woods that are employed in the 
arts, therefore a few only are selected, or such as are com- 
monly employed in the United Kingdom for purposes where 
strength is the primary object, viz. ash, beech, elm, fir, horn- 
beam, mahogany, oak, and teak. 

Ash. 

Ash is a coarse wood, but possessed of considerable 
strength, and is distinguished for its great toughness and 
elasticity, and is usually employed where severe shocks and 
wrenches have to be encountered, such as for agricultural 
implements, the felloes and spokes of wheels, and the shafts 
of carriages, for hammer shafts, and for spring purposes 
generally wherever wood is employed for that purpose. 

From its great flexibility it is seldom employed where 
rigidity is a desideratum. The combination of strength 
with flexibility is the characteristic of ash, and when the 
wood is from a young tree, or a tree not too old, it is an 
invaluable wood in many respects ; but as the tree becomes 
older, the change to brittleness sets in and soon renders it 
less valuable. It is also remarkable for its endurance when 
kept dry, but when exposed to damp' or to wet it rapidly 
decays. The numerical value of its properties, as will be 
seen by the Tables, varies considerably, but in general terms 
it may be stated that, as compared with oak, good ash has 



Timber. 109 

frequently a still greater tenacity and likewise a greater 
degree of toughness, but from its flexibility, especially when 
young, it has considerably less stiffness, which unfits it for 
many purposes. 

Beech. 

Beech has frequently considerable strength, and is chiefly 
distinguished for its uniformity, its smoothness of surface, 
and closeness of grain. It likewise possesses no little 
beauty, and takes a good polish, more especially when its 
silver grain is skilfully exposed. When well seasoned and 
not too old it is frequently used for the cogs of mill gearing, 
and is usually considered by millwrights as next to horn- 
beam, both in strength, toughness and general suitability 
for that purpose. It requires, however, to be kept very dry, 
for in damp situations it quickly wears out, but, when beech 
is immersed in water constantly, its endurance is consider- 
able. The strength of beech is nearly the same as that of 
oak ; it is also tougher, but its stiffness is inferior to that 
of oak, even to the extent of 25 per cent. 

Elm. 

Elm, although a cross-grained, rough wood, and mostly 
used for rough purposes, is yet held in great estimation for its 
toughness and non-liability to split by the driving of bolts. 
It is much used in the construction of blocks for pulley- 
tackle, for heavy naval gun-carriages, and for the naves of 
carriage-wheels. It is a wood which is little affected by 
constant immersion in water, but decays rapidly when alter- 
nately wet and dry, and consequently is not very durable 
for purposes involving exposure to a wet climate. Its chief 
defect in ordinary use is its great liability to warp and twist 
and get out of form ; and, as regards strength, toughness, 
and rigidity, it is inferior to oak, as well as in almost every 
other respect. 



no On the Strength of Materials. 

Pine and Fir Wood. 

The fir and pine woods are members of a large family, 
and are of great variety, and differ much in most of their 
properties. These classes of timber, in addition to being 
employed for building purposes, are likewise the chief 
materials that are used in great works, where the question of 
strength combined with cost becomes the most prominent 
consideration. The most durable varieties are the larch, 
the pitch-pine, and the firs from Memel and Norway, and 
are valued mostly on account of the large quantity of resin, 
pitch, and turpentine which they contain. The Canadian 
pine, variously termed white or yellow, is not a strong wood, 
but it is much used by engineers for making patterns or 
models, on account of its smoothness of surface, its non- 
liability to warp, its comparative freedom from knots, and 
the facility with which it can be cut. The white or yellow 
pine is not nearly so strong or so stiff as oak, yet sometimes 
it is almost equal to it in its tenacity and toughness. 

In such a large family as that of the resinous firs and pines, 
there is almost an equal variation in their strength, tough- 
ness, and rigidity. Much of the European wood, such as 
that from Memel and from some parts of Scotland, is often 
superior to oak, while at other times it is inferior, more 
especially in regard to stiffness, as will be seen by the Table. 

Hornbeam. 

Hornbeam is a wood which is comparatively little used, 
except by engineers, for the teeth or cogs of wheels and for 
mallets, for which purposes it is perhaps superior to all other 
woods, and this is mostly due to its great toughness and re- 
markably stringy coherence of fibre. Its cohesive strength 
and other properties depend much upon its age as a plank, 
and still more on the age of the tree from which the plank 
was taken. When in the most favourable condition, it is 
fully equal to the average of oak (even when considered 



Timber. I r I 

merely as a wood), but when cut from older trees, and when 
over-seasoned, it is frequently found worthless, and has soon 
to be renewed. When of proper age and quality, it has no 
equal for its own special purposes. 

Mahogany. 

Mahogany is a beautiful close-grained wood, but is used 
not so much on account of its strength, but more frequently 
because of its non-liability to shrink, warp, or twist, and 
from the peculiar property of taking a firm hold of glue. In 
the last respect it is superior to any other wood. Mahogany 
differs greatly in regard to its closeness, hardness, strength, 
and beauty. That from Honduras, called ' bay-wood,' is 
much inferior to that called ' Spanish ' mahogany, which 
comes from the West Indies ; the former is much used in 
the construction of light textile machinery, but chiefly on 
account of its cheapness, and the latter is used for furniture 
or for other ornamental purposes. As regards strength, this 
wood is inferior to oak in ail respects, and its great cha- 
racteristic defect is unsuitability for exposure to the weather, 
or indeed for any purpose where it is made alternately wet 
and dry. When so subjected, it rapidly decays, and loses 
all its good qualities. 

Oak. 

Oak, taken as a whole, is one of the strongest and most 
durable of woods, and is especially adapted for exposure to 
the weather of a damp climate, and is indeed suitable for 
almost every purpose where the properties of strength, stiff- 
ness, and toughness, combined with endurance, are required. 
Its value for ship-building is proverbial, and its employment 
for the staves of casks, for trenails, for carriage-wheels, and 
for all such purposes requiring lightness and strength in 
combination it is equally useful. From time immemorial it 
was esteemed the best timber for heavy roofs, and the con- 



112 On the Strength of Materials. 

dition in which some of these grand old roofs have reached 
our era, fully attests the wisdom of the selection. 

Oak is found of many degrees of quality, but probably 
none, taking every property into account, is superior to that 
which grows in England, and which is perhaps more durable 
than any other. Some of the foreign oaks are as good in 
some respects, but, as a whole, English is the best. 



Teak. 

Teak is a most valuable wood, and is fitted for most pur- 
poses where oak is employed. It is equally durable, but is 
more liable to split by the driving of bolts, and is not so 
well adapted for a sudden jar or wrench. Its great dura- 
bility is partly due to the large quantity of oil which it con- 
tains ; the oil likewise is found to prevent the rusting of the 
iron bolts employed in framing it. For gun-carriages or for 
similar purposes, its value is increased by the small amount 
of shrinkage which takes place, even after long exposure to 
a hot climate. In this respect it is superior to oak ; and it 
has another property, it is not much exposed to attack by 
the worm of tropical countries, which is a great advantage. 
Teak, as a rule, is superior to oak, both in regard to 
tenacity and stiffness, but is inferior as regards toughness ; 
but when those qualifications are required in combination 
with, endurance in a tropical country, it has the superiority, 
and is therefore preferred. 

The foregoing remarks being of a general nature, can only 
be considered as preliminary to a study of the Tables which 
follow. In past times, an immense number of experiments 
have been made upon wood, more especially in regard to 
its tensile strength. The next Table contains the result of 
experiments made at different times to ascertain the general 
range of the ultimate cohesion or tensile strength of the 
foregoing descriptions of timber. 



Timber. 



"3 



TABLE XVIII. 

These results have been collected from various sources, but chiefly 
from the experiments made by Barlow, Bevan, and Muschenbroek. 



Timber. 


Ultimate tenacity in lbs. per square 
inch of section. 


Ash . 






from 19,600 to 15,784 


Beech 






,, 22,200 ,, 11,500 


Elm . 






„ 14,400 „ 13,489 


Fir .... 






,, 18,100,, 7,000 


, , American 






12,000 


,, Memel 






11,000 


„ Riga . 






12,600 


,, Mar Forest . 






12,000 


,, Larch . 






10,200 


Hornbeam . 






from 20, 240 to 4, 2 5 3 


Mahogany . 






,, 21,800 ,, 8,000 


Oak . 






,, 19,800 ,, 9,000 


, , English 






15,000 


,, African 






14,400 


, , Canadian . 






12,000 


, , Dantzic 






14,500 


Teak 






from 15,000 to 8,200 



The next Table contains the result of experiments made 
to ascertain the average resistance to ultimate crushing of 
the foregoing descriptions of timber in the direction of the 
fibre, when in the form of short pillars. 



ii 4 



On the Strength of Materials. 



TABLE XIX. 

These results are mostly derived from the experiments of Hodgkinson. 



Timber. 


Average resistance to crushing stress, 
in lbs. per square inch of section. 


Ash . 

Beech 
Elm . 
Fir . 
Hornbeam 
Mahogany- 
Oak, English 
,, Dantzic 
Teak 








from 9,363 to 8,683 

» 9,363 „ 7,733 

10,331 

from 6,819 t0 5,375 

„ 7,289 „ 4,533 

8,280 

from 10,058 to 6,484 

7,731 
12,101 



This Table contains the result of experiments made by 
Rennie, to ascertain the average resistance to crushing in 
the direction of the fibre of short pillars of timber. 



TABLE XX. 

Size of specimens, i-inch cubes. 



Timber. 


Average resistance to crushing stress, 
in lbs. per square inch of section. 


Elm 

American pine .... 
White deal .... 
English oak .... 


1,284 
I,6o6 
1,928 
3,860 



These experiments show a considerably less result than 
those made by Hodgkinson, and it is scarcely possible to 
reconcile the discrepancy between the two Tables ; but most 
probably it could be easily explained if all the facts of the 



Timber. 



"5 



experiments were fully known, as everything depends on 
the amount or degree of the crushing action that was 
effected in the several experiments. 

Timber is sometimes subjected to a crushing force in the 
other direction ; namely, at right angles to the fibre, as in 
the case of a wedge, or when baulks of timber are used to 
support great weights, or when two pieces are framed and 
bolted together or otherwise. In regard to this important 
point, however, there are comparatively few experiments 
recorded, and, as a rule, those which are recorded are not 
very definite. All are familiar with the fact, that a very 
small force will be sufficient to indent wood to some appre- 
ciable extent. The precise force that will crush a cubic 
inch perceptibly — say 10 3 o0 ths of an inch — may be said to 
range from 500 lbs. to 1,500 lbs., according to the hardness 
or softness of the specimen. 

The following Table contains the results of experiments 
made by Hatfield, to ascertain the force required to compress 
timber to a depth of -^tii of an inch, in a direction at right 
angles to the fibre : — 



TABLE XXI. 



Timber. 


Stress in lbs. per square inch 
required to crush fibres trans- 
versely, and to produce an 
indentation of -^ of an inch. 


Specific 
gravity. 


Spruce fir 
White pine 
Mahogany, Bay-wood 

,, St. Domingo . 
Oak ... . 
Ash . 
Lignum vitse . 


500 

600 

1,300 

4,3°° 
1,900 
2,300 
5,800 


•369 
•388 

'439 
•837 
•612 

•517 

1-282 



I 2 



n6 On the Strength of Materials. 



Shearing or Detrusion of Wood. 

In the application of timber to form framings for ma- 
chinery, in the construction of roofs of houses, and in 
scaffoldings, too much reliance is frequently placed by the 
carpenter, upon the support which is understood to be derived 
from an abutment against a notch cut into the solid wood, 
thereby bringing into play the end shear of a portion of the 
material, in the direction of the fibre. From experiments 
made by Barlow, the strength of timber thus strained is 
only about Ju-th of the tenacity of the same wood in the 
direction of its length. 

The assumption that wood may be treated like metal in 
this respect is wrong. With metals, the resistance to 
tension and detrusion are nearly alike both ways, the solid 
' joggles ' left upon an iron casting give an abutment nearly 
equal to the tensile strength of the metal ; but with wood 
similarly arranged it is only equal to the -^th part of the 
tensile strength. This deficiency is usually compensated 
for by the extra length given to the part which has to be 
detruded ; still, the weakness of timber in this respect should 
be noted. 

The following Table refers to the transverse strength of 
timber when used as a beam. The results are collected 
from a variety of sources ; and as the experiments were made 
with specimens of varied dimensions, the whole have been 
reduced to one standard, for the sake of comparison : — 



Timber. 



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On the Strength of Materials, 







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Timber. 



121 



The attention of the student is particularly directed to 
column 5 of the foregoing Table, which will furnish him 
with much useful knowledge on the transverse strength of 
wooden beams, in a small compass, and will enable him to 
calculate either the strength or required dimensions of any 
other rectangular beam of any of the kinds of wood therein 
specified. 

In Chapter XII., upon the strength of structures, the 
principles which regulate the strength of such beams are 
fully stated. It will be sufficient here to remark, that by 
taking the beam in column 5, which is 1 foot long and 
1 inch square, as a standard, the student can ascertain the 
strength of any other rectangular beam, by simply multi- 
plying the strength of the standard beam by the breadth, 
and the depth squared, both in inches, and then dividing 
the product by the length, in feet, of the given beam, the 
strength of which he wishes to ascertain. 

Table showing approximately the mean breaking weight 
of beams of timber, 1 foot long and 1 inch square, supported 
at both ends and loaded at the centre, deduced from the 
experiments enumerated in Table XXII. : — 

TABLE XXIII. 





Mean breaking 




Mean breaking 


Timber. 


weight of beam 


Timber. 


weight of beam 




in lbs. 




in lbs. 


Ash . 


690 


Oak— 




Beech . 


625 


, , Adriatic 


460 


Elm . 


405 


,, African 


855 


Fir — American 


524 


,, Canadian 


580 


, , Christiana . 


574 


,, Dantzic 


513 


,, Larch . 


440 


,, English 


591 


,, Mar forest . 


381 


Mahogany 


557 


,, Memel. 


561 


Teak 


814 


„ Riga . 


457 







The above Table can only be considered as available for 
approximate calculations. 



122 On the Strength of Materials. 



CHAPTER IX. 

TRANSVERSE STRENGTH OF IRON AND RESISTANCE TO 
IMPACT. 

The transverse strength of materials, more especially that 
of cast iron, in the form of beams and girders, has been 
closely investigated by a number of scientific men, particu- 
larly by Sir William Fairbairn, Mr. Hodgkinson, and the 
Railway Commissioners. The subject will be treated of in 
Chapter XII. ; but it will be convenient to give here an 
abstract of the results of various experiments, on the trans- 
verse fracture of bars of different materials. 

A bar laid horizontally upon supports and loaded at the 
centre bends, and ultimately breaks, by transverse strain. 
The two points most important to be observed are the 
breaking weight and the deflection of the bar. Some results, 
obtained in experiments of this kind, are given in the subse- 
quent Tables. 

The following Table contains a synopsis of the results of 
a series of experiments, carried out under the direction of 
the Commissioners appointed to enquire into the Applica- 
tion of Iron to Railway Structures. Their object was to 
determine the transverse strength and ultimate deflection of 
cast-iron bars, when subjected to a statical load placed at 
the centre : — 



Transverse Strength & Resistance to Impact. 123 



TABLE XXIV. 



Name of Iron. 


Size of 
bar in 
inches. 


Distance 
between 
supports 
in feet. 


Weight 
of bar be- 
tween sup- 
ports in lbs. 


Breaking 
weight 
in lbs. 


Ultimate 
deflection 
in inches. 


Blaenavon 
No. 2. 


I inch 
square. 


4* 


I3-49 

r 3 - 34 
13-02 
13-06 


461 

359 

437 
423 


1-796 

I-3I5 
I -8 5 
1-6917 


Mr. Stirling's. 
Calder No. I, 
with 20 per 
cent, of malle- 
able iron scrap. 


2 inches 
square. 


9 


1 1 1 -07 
114-41 
1 1 1 -46 
112-91 


2,411 

1,837 
2,083 

2,364 


3-I03 

2-227 

2-395 
2-883 


Blaenavon 
No. 2. 


2 inches 
square. 


9 


107-6 
109-6 
108 -o 
108 -o 


1,249 
1,414 
1,121 
1,097 


2-906 
3-486 
2-527 
2-498 


Blaenavon 
No. 2. 


3 inches 
square. 


13* 


358-29 
365 -39 
367-29 
365-06 


2,698 
2,671 

3,389 
2,686 


4-863 
4-39o8 
5-024 
4-39I 



Abstract of the results of experiments made by the above 
Commissioners to find the relative transverse strength of 
cast-iron bars, of various sizes, but similarly proportioned 
in all their dimensions : — 

Note. — The horizontal pressures in the following Table were com- 
puted from the vertical pressures, by taking into account the weight 
of the bar itself, which would not have any tendency to weaken the 
bar when pressed in the horizontal direction, but of course acted as so 
much additional load when the bars were pressed vertically. 



124 



On the Strength of Materials. 

TABLE XXV. 



Size of bar. 


Vertical pressures. 


Horizontal pressures 
computed from the 
vertical pressures. 


Mean 
strength 
in lbs. 


Mean ul- 
timate de- 
flection in 
inches. 


Mean 
strength 
in lbs. 


Mean ul- 
timate de- 
flection in 
inches. 


3 bars 4^ feet span and 
I inch square. 


440 


1779 


447 


1-808 


6 bars 9 feet span and 
2 inches square. 


1,338 


3'0035 


1,394 


3-126 


4 bars 13^ feet span and 
3 inches square. 


2,86l 


4-667 


3,043 • 


4-966 


3 bars 6| feet span and 
3 inches square. 


6,117 


1-2916 


6,207 


1-311 



This Table shows, first, that the strength of the similar 
bars, 1 inch, 2 inches, and 3 inches square, and 4^- feet, 
9 feet, and 13^ feet span, to resist a horizontal pressure, are 
respectively 447, 1,394, and 3043 lbs. ; but if the elasticity 
of the bars had been perfect, their strengths should have 
been as the squares of their linear dimensions, namely, in 
the ratio of the numbers 1, 4, and 9. Dividing the strengths 
by these numbers, the quotients ought, on the supposition 
of perfect elasticity, to be equal. We find, however, 

447 ri = 447 for 1 inch bars. 

1,394 -r 4 = 349 for- 2 inch bars. 

3,943-^9 = 33 8 for 3 in ch bars. 
The quotients being unequal, and the greatest deviation 
being in the case of the smallest bar. Probably this is due 



Transverse Strength & Resistance to Impact. 125 

to the more rapid cooling of the small bars, which tends to 
increase the strength and hardness of the metal. The 
Table shows, also, that for square bars of constant length 
between the supports, the transverse strength varies nearly 
as the cube of the side of the square. 

Abstract of experiments made for the Railway Com- 
missioners on the resistance of cast-iron bars to long-con- 
tinued impact, from a ball striking horizontally against the 
middle of the bar : — 



TABLE XXVI. 



Distance 


Side of 


Weight 


Velocity of 


Assigned 


Number 






between 
supports. 


square 
of bar 
inches. 


of ball 
in lbs. 


impact in 
feet per 
second. 


deflection 
in inches. 


of 
blows. 


Effect. 


Remarks. 




3 


151* 


8-812 


g- or 1-5 


I,o8 5 


broken. 


slightly 
defective. 




3 


i5i* 


9-4899 


i or 1 -5 


4,000 


not broken. 






3 


603 


3-6156 


i or 1-5 


4,000 


» ? 




*3i ft- 


3 


603 


4-5754 


& or 1 -875 


1,350 


broken. 


slightly 
defective. 




3 


i5ii 


137834 


* or 2-25 


127 


5 ? 


j> 




3 


603 


5^39 


| or 2-25 


3,026 


" 






2 


75* 


6-2132 


^ or 1 -oo 
£ or 1 -oo 


4,000 


not broken. 






2 


603 


1-8071 


4,000 


,, 






2 


75* 


— 


h or 1 -50 


229 


broken. 


defective. 


9 ft. 




75* 


9-3204 


* or 1-50 


1,282 


,, 


slightly- 


2 












defective. 




2 


603 


2-5284 


* or 1 -50 


3.695 


j » 


j? 




2 


75* 


11-693 


§ or 2 -oo 


127 


>» 






2 


603 


3-5872 


| or 2 -oo 


474 


>5 






1 


75* 


2-1461 


£• ° r -50 


4,000 


not broken. 




4| ft. 


1 


75* 


3-0368 


* or 75 


4,000 


,, 




1 


75* 


3-5018 


& or -875 


3,700 


broken. 


slightly 


1 












defective. 

1 



126 



On the Strength of Materials. 



One bar only, and that a small one, stood 4,000 blows, 
each blow bending it through half its ultimate deflection with 
a statical breaking weight ; but all the bars, when sound, stood 
that number of blows, each blow deflecting them through -J-rd 
of their ultimate deflection. A cast-iron bar will, however, be 
bent through -Jrd of its ultimate deflection with less than -Jrd 
of its breaking weight, laid on gradually, or \Xh. of the break- 
ing weight laid on at once — hence the prudence of making 
beams capable of bearing more than six times the greatest 
weight which will be laid upon them. 

Abstract of results of experiments on vertical impacts, 
upon unloaded and loaded beams of cast iron (Blaenavon, 
No. 2), 13 ft. 6 ins. between supports and 3 ins. square; the 
falling weight being 303 lbs. : — 





TABLE XXVII. 






Weight of 




Height of 
fall necessary 


Velocity of 

impact due 

tothat 

height. 


beam 
in lbs. 


Additional load on beam in lbs. 


to break the 
beam in 
inches. 


376! 


nil. 


28* 




382 


4 lbs. at centre. 


33 


I3'3 


375i 


28 lbs. at centre. 


42 


15-0 


387 


166 lbs. spread over the beam 
+ 4 lbs. at centre. 


48 


16-0 


386 


3895 lbs. spread over the beam 
+ 4 lbs. at centre. 


48 


160 


379 


391 lbs. spread over the beam 
-H 4 lbs. at centre. 


66 


18-8 


382 


956^ lbs. spread over the beam 
+ 4 lbs. at centre. 


60 


17-9 



It will be seen that loaded beams resisted better than 
unloaded ones. 

The deflections were found to Vary nearly as the velocity 
of impact. 

The sets were very great, but did not appear to injure the 
strength of the bars more than in ordinary cases, with an 
unloaded beam. 



Transverse Strength & Resistance to Impact. 127 



Synopsis of experiments on the transverse flexure of five 
bars of Blaenavon iron, No. 2, cast to be i\ inches x 1^- 
inch in section, and 13 feet 6 inches between supports, 
the pressure being applied in the direction of their least 
dimension : — 

TABLE XXVIII. 



Weight applied 


Mean deflection 


Mean set after 




acting horizontally 


after 5 minutes 


5 minutes in 


Remarks. 


in lbs. 


in inches. 


inches. 




28 


•l8l 


•OOl6 




56 


'3754 


•0068 




112 


7686 


•OI92 




168 


1-184 


•O468 




224 


1-632 


•0914 




280 


2-I05 


•i486 


Limit of elasticity, 


336 


2*604 


•2266 


^ of ultimate or 


392 


3-169 


•3292 


breaking weight. 


448 


3756 


■4574 




5°4 


4-402 


•6078 




560 


5-03S 


7854 




616 


5777 


I-0 3 8 




672 


6-565 


I-287 




728 


7-610 


1-707 




784 


873 


2-186 




840 


9-887 


2-691 


Nos. 1,3,4,5, broke. 


896 


107 (No. 2) 


3-006 




934 


— 


No. 2 broke. 





Similar experiment with bars 2 inches x 1 inch, and 
9 feet between supports : — 



TABLE XXIX. 



Weight applied 
acting horizon- 
tally in lbs. 



28 

485 



Mean deflection after 
5 minutes in inches. 



Mean set after 5 
minutes in inches. 



•235 -002 

mean breaking weight of the sound 

bars. 



Remarks. 



Limit of elas- 
ticity, ^ of 
ultimate or 
breaking 
strength. 



128 On the Strength of Materials. 

These Tables show the apparently very great want of 
elasticity of cast iron : a permanent set being attained in one 
case with ^-th of the ultimate breaking weight, and in another 
case with ^th of the ultimate breaking weight. 

The following results are intended to show the effect pro- 
duced by repeated deflection — the experiments having been 
made for the Railway Commissioners. 

Cam experiments on the deflection of cast iron bars, 13 
feet 6 inches long, and 3 inches square : — 

The step cam gradually deflected the bars to the required 
amount, and then allowed them to spring back instantly to 
their original position, so far as they would do so. 

The rough cam was simply a toothed excentric, working 
into a rack fixed upon the bar, it deflected and also allowed 
the bar to return to its original position, gradually, and 
imparted, by its roughness, a highly vibratory motion to 
the bar. 

First Experiment. — Three bars of No. 2 Blaenavon iron 
were subjected to 10,000 deflections by the rough ca?n, each 
deflection amounting to that caused by -^rd of the statical 
breaking weight. The permanent set at 100 deflections was 
found to be '2 inch, -17 inch, and '19 inch respectively, and 
there was no increase in the permanent set after 100 deflec- 
tions. These bars required the same weight to break them 
after the experiment, as similar bars which had not been so 
treated, showing that they were uninjured by the experiment. 

Second Experiment. — This was similar to the first experi- 
ment, but the deflections were made with a step cam. The 
permanent sets at 150 deflections were *i6 inch, -13 inch, and 
•12 inch. No increase was observed after 150 deflections, and 
the bars were apparently not weakened by the experiment. 

Third Experi?7ient . — Similar bars to the above were de- 
flected to the amount caused by Jrd of the statical breaking 
weight, by the step cam. 



Transverse Strength & Resistance to Impact. 1 29 

No. 1 bar broke after 51,538 deflections — (fracture good) 
— bar weakened by experiment. 

No. 2 bar broke after 25,486 deflections — (flaw). 

Xo. 3 bar not broken after 100,000 deflections — bar not 
weakened by experiment. 

Permanent set at 150 deflections, -08 inch, -2 inch, -08 
respectively — no further increase. 

Fourth Experiment. — Two similar bars of Clyde iron, No. 
3, deflected to the amount caused by \ the statical breaking 
weight by the rough cam. 

No. 1 bar not broken after 30,000 deflections — (bar not 
weakened). 

No. 2 bar broke after 28,602 deflections. 

Permanent set at 1,000 deflections, '35 inch and "37 inch 
respectively — no further increase. 

Fifth Experiment. — Three bars of No. 2 Blaenavon iron, 
deflected to the amount caused by \ the statical breaking 
weight by the step cam. 

No. 1 bar broke after 617 deflections. 

No. 2 bar broke after 490 deflections. 

No. 3 bar broke after 900 deflections. 

Permanent set at 150 deflections, '44 inch, '37 inch, and 
•37 inch, no further increase. 

Sixth Experiment. — Bar of wrought iron, 9 feet long and 
2 inches square, showing statical weight required to obtain 
certain deflections : — 

TABLE XXX. 



Deflections, 
inches. 


Weights, 
lbs. 


Permanent 
set. 


Remarks. 


'333 

•666 

•833 
i-ooo 
i-8 


507 

926 

1,121 

1,364 

1,950 


O 
O 
O 
•054 

•86 


After the bar had 1,950 lbs. on, it 
suddenly gave way ; it did not 
break, but no farther weight 
could be applied with certainty. 



130 



On the Strength of Materials. 



Seventh Experiment. — This was a valuable experiment ; it 
showed that a wrought iron bar, 9 feet long and 2 inches 
square, deflected to -833 inch (about fths of the strain that 
permanently injured a similar bar), withstood 100,000 de- 
flections : permanent set '15 inch ; bar uninjured. 

Eighth Experiment. — Five similar bars, deflected by the 
step cam : — 

TABLE XXXI. 



No. of bar. 


Amount of 


Number of 




deflection. 


deflections. 


Permanent set. 




inches. 






I 


•33 


io-ooo 


O 


2 


•66 


io-ooo 


O 


3 


•83 


io-ooo 


O 


4 


i-oo 


io-ooo 


•06 


5 


2'00 


IO 


'3 






50 


"54 






IOO 


•69 






I50 


•84 






200 


•98 






300 


I-8 4 



CHAPTER X. 



RESISTANCE TO TORSION AND SHEARING. 

The torsional resistance of different materials has not re- 
ceived so much investigation as the tenacity, compressive 
resistance, and transverse resistance of materials, and the 
results of the few recorded experiments are very discordant. 
Still there are sufficient data to show the relative value of 
the different metals, and their approximate resistance to 
torsion. 

It is chiefly in designing the shafting of mills and factories 
that we require to know the torsional strength and stiffness 
of bars. Such shafting consists almost always of cylindrical 



Resistance to Torsion and Shearing. 131 

bars of greater or less length, and it is the agent by which 
the power of the steam-engine or other motor is distributed 
to the machinery, spread frequently over a large area. But 
the crank shafts of engines, the propeller shafts of screw 
steam vessels, the spindles or shafts of cranes, and many 
other parts of machines are also subjected to torsion. 

The most important result of the experiments on torsion, 
which should be remembered in designing shafting, is this' 
that the strength of cylindrical bars, when twisted, is propor- 
tional to the cubes of their diameters. Hence, if we know 
the torsional strength of any one cylindrical bar, say of 1 
inch in diameter, when made of cast iron, wrought iron, or 
steel, we can calculate from it the strength of shafts of other 
dimensions of the same material. If the strength of such a 
shaft or bar of 1 inch in diameter is represented by 1, that 
of a shaft 2 inches in diameter will be equal to 8, of 3 inches 
to 27, and so on. In the case of hollow shafts, by simply 
cubing the exterior diameter and then deducting the cube 
of the interior diameter, the difference will give the relative 
value of the shaft, as an agent to transmit power or motion. 

The torsional strength of wrought iron has received more 
attention than that-of any other material, because modern 
shafting is chiefly made of that metal. We may therefore 
indicate, first of all, the results obtained in experiments with 
wrought iron. Many experiments on torsion have been 
made on cylindrical bars 1 inch in diameter, the load being 
applied by a lever, the length of which is 12 inches measured 
from the centre of the bar. We may therefore express the 
relative resistance to torsion of different bars by stating the 
weight which twists them asunder when applied in the way 
indicated. The amount of load which is required to pro- 
duce rupture is usually reckoned at an average of 1,000 lbs. 
on the end of the lever, but will necessarily deDend on the 
quality of the iron as well as other conditions. In one 
instance, where a bar or strip of iron was cut out of a welded 
coil, across the welds, rupture took place with less than 



1 32 On the Strength of Materials. 

400 lbs., no doubt in consequence of a defective weld. The 
highest torsional strength here quoted, namely, 1,000 lbs. 
acting at a leverage of one foot, is derived from experiments 
made with specimens of an exceptionally good quality of 
wrought iron • 700 lbs. to 800 lbs. is probably nearer to the 
average strength of good common wrought iron. 

Wrought iron is better for shafting than cast iron, because 
of its greater torsional strength. In consequence of the 
greater strength of wrought iron, shafting made of that 
material is lighter than cast-iron shafting, and this is a 
matter of great importance, because the friction of shafts on 
their bearings is directly proportional to their weight. As 
will be shown, however, presently, the stiffness of wrought- 
iron shafting is not much greater than that of cast-iron 
shafting, and permanent set commences with less stress in 
the former case than in the latter. 

Cast iron, even more than wrought iron, varies in quality. 
From some experiments made with specimens of cast iron, 
the torsional resistance was equal to 900 lbs. on the end of 
the lever ; but the highest result obtained at Woolwich, with 
a specimen which was considered a particularly good sample 
of cast iron, gave only 670 lbs., and there are some kinds of 
cast iron which would not afford a resistance equal to the 
half of even that weight. Hence it may be convenient to 
assume the torsional strength of a cylinder one inch in dia- 
meter of good cast iron as equal to from 650 lbs. to 750 lbs., 
according to the quality and the conditions of the casting. 

Some experiments were made in America with cast iron 
under torsion, the bar being 8 diameters long. The force 
required to give to the bar a permanent set of \° was equal 
to T 7 Q-ths of the force required to twist it asunder ; the same 
amount of set is given to wrought iron with a less stress, or 
about ^ths of the ultimate twisting force. 

From some experiments made by Sir W. Fairbairn with 
cast iron, some specimens were higher, and some were lower, 
but the mean was 733 lbs. on the end of the 12-inch lever. 



Resistance to Torsion and S /tearing. 133 

Cast steel, being superior to wrought iron in most other 
respects, is also stronger in its resistance to torsional stress. 
From some experiments which have been made with steel 
of high quality, it was found that a cylinder one inch diam- 
eter required 1,900 lbs., acting at a leverage of one foot, to 
twist it asunder. Such a high result, however, must be rare, 
and, judging by the result of an experiment made with part 
of the tempered steel lining of a gun, which only required 
1,355 ^s., we may safely consider the value of the average 
quality of steel, as much less than 1,500 lbs. on the 12 -inch 
lever; that of good Bessemer steel being 1,1 50 lbs. 

Cylinders of wrought copper, one inch in diameter, require 
a load varying between 400 lbs. and 450 lbs. on the end of 
the 1 2 -inch lever. 

The foregoing remarks refer to the ultimate torsional or 
breaking strength ; but, as before remarked with regard to 
the other properties, the limit of torsional elasticity is the 
chief point for the engineer to keep in mind, regarding 
which, however, there are not sufficient reliable data on 
which to lay down simple rules. Hence, it is usual not to 
load shafts with more than -J^-th of the weight that would be 
required to produce ultimate rupture \ there are some, how- 
ever, who are satisfied with the half of that margin. 

The torsional stiffness of a long line of continuous shafting 
is dependent on the length ; but the length of the line affects 
the amount of twist only in this way, that the total twist of 
the entire length is the sum of the twists of each portion of 
the length. The amount of twisting of a given length is 
proportional to the twisting force, so long as that force does 
not exceed the elastic limit of the material. If it does, a 
permanent twisting is produced, similar to the permanent 
set in experiments on tension. 

In the case of long shafting, the torsional stiffness is of 
more importance, practically, than the torsional strength. If 
the shaft is deficient in stiffness, so that when working it 
is twisted through a large angle, it runs in a jerky manner, 



134 On the Strength of Materials. 

and the machines driven by it work badly. In long shafting, 
it is usual to secure sufficient stiffness by restricting the 
angle of torsion to some definite limit, say to ^° per yard 
length of the shaft, and to secure this amount of stiffness a 
larger shaft is often required than would be needed, if 
strength alone were considered. The resistance of shafts of 
equal stiffness, in this sense, is proportional to the square 
of the area — that is, a 2-inch shaft will transmit 16 times 
the force which would be transmitted by a i-inch shaft 
without being twisted through a greater angle. 

In the shafts or spindles of cranes, torsion, and not stiff- 
ness, is the prominent point, on account of their shortness, 
which does not give sufficient play to elasticity to make the 
want of stiffness objectionable. 

When a tie-rod, or a strut, or a long shaft, is so constructed 
that certain parts have a larger or smaller diameter than 
other adjoining parts, it is evident that the strength cannot 
be greater than that of the weakest portion. In practice, 
however, it is found that if the small part of the shaft passes 
abruptly into the larger part, it is even less strong than its 
dimensions would indicate, or rather, it is more correct to 
say, that fracture takes place with a less load than in an 
uniform bar, of the same section as the smallest part of the 
•shaft. More especially is this the case with the bearings of 
shafts, if the re-entrant angle of journals or corner of union 
is left square, instead of being rounded off. This discrepancy 
arises from two obvious causes : first, because the small part 
is the weakest portion of the bar, and consequently has more 
than its share of the elastic work to perform ; and secondly, 
because at the junction of the two diameters, the fibre or 
molecules do not spread out to take hold of the larger 
diameter. In practice, it is found that this defect is obviated 
to some extent by rounding the corner, and the risk of 
fracture is thus reduced. 

In considering the diameter to be given to a shaft, the 
pull or transverse strain which will come upon it in the 



Resistance to Torsion and Shearing. 135 

middle of the distance between the bearings must also be 
taken into account. A comparatively small ■ shaft may be 
strong enough to transmit the necessary power, yet not 
strong enough to bear the stress of several tight straps, 
causing deflection in addition to twisting, and hence the 
strength of the shaft has so far to be reckoned as a beam, 
irrespective of torsion, and a suitable diameter provided 
accordingly. 

The results of experiments made with round bars of i-inch 
diameter, and with a lever of 12 inches in length, have been 
given, and it has been stated that the strength of other bars 
is to that of a i-inch bar as the cubes of the diameters. It 
has also to be observed, that the resistance of the shaft to a 
given load is inversely as the radius of the lever. With 
a lever 6 inches long, or half the standard length of 12 inches, 
twice the load must be applied to break the bar. With a 
lever 24 inches long, or double the standard length, only half 
the load would be sufficient to break the bar. Keeping 
this in view, we may compare the torsion produced by 
wheels or pulleys of different diameters. 

In practical operations, it is seldom that the engineer can 
obey the laws of correct proportion as strictly as he would 
desire, on account of other considerations, which step in to 
modify his proceedings. If, for example, a long shaft were to 
be constructed, of sectional area in exact proportion to the 
strain anticipated at each point, the shaft ought to be largest 
at the driving end, and gradually diminished by tapering down 
to the other extremity. In practice, however, this would be 
found inconvenient, because the arrangement involves a 
multifarious assortment of pulleys, with bores of different 
diameters, for the reason that, in the conduct of a factory, 
such pulleys have frequently to be transposed from one 
point of the shaft to another point, in order to suit the vary- 
ing circumstances of the machinery to be driven. To 
obviate this difficulty, true proportion in the shaft is con- 



1 36 On the Strength of Materials. 

stantly departed from, and the shaft usually made of the 
proper strength at the driving end, to transmit the required 
amount of power, and then reduced by stages, at, say every 
hundred feet, or even less. This implies greater cost for 
shafting in the first instance, but the future facility which it 
affords is more than an equivalent to the original outlay. 

In the working of a long line of shafting, the elasticity is 
observable, and even becomes inconvenient and prominent 
when the shaft is made too light. The following interesting 
experiment was made, in connection with the driving of such 
a long line. The shaft was originally driven from one 
end only, and afterwards means were adopted to drive 
from both ends; but the irregularity of the motion, with 
the new arrangement, gave rise to a considerable dis- 
turbance in the middle of the shaft, which made the new 
arrangement equally unsatisfactory with the previous one. 
The shaft was then cut in the middle, and driven at the same 
velocity from both ends. Long pointers were fastened to 
each shaft at the point where they came together, in order 
to show the divergence of their motion ; the cause of the 
previous disturbance was soon made evident, for the two 
bars, although running at the same speed in revolutions per 
minute, did not keep true time in their twisting, the two 
pointers were seldom together, being sometimes to the 
extent of half a revolution apart, sometimes one, and at 
other times the other, in advance, the cause of disturbance 
being the ever-changing strain, due to variations in the 
stress of the work done at various points ; stiffness and 
steadiness can only be attained by an increase of substance 
beyond that necessary for strength; the line was evidently 
deficient in stiffness, notwithstanding its abundance of 
strength. 

When a bar of iron is wrenched asunder by torsion, the 
break or rupture must be considered as a shear. Where a 
given area of metal has to be sheared, it is found that the 
force required is nearly the same as that necessary to tear 



Resistance to Torsio7i and Shearing. 137 

asunder a piece of the same material of equal area. The 
shearing force, however, is rather less than the tenacity, 
therefore, to shear a square inch bar would require a force 
of between 18 and 24 tons, according to quality. The 
torsional strength of the bar may be calculated from this 
value of the shearing force, but practically the question does 
not present itself in this form, and it is more simple to con- 
sider torsion in connection with forces acting at the end of 
a lever. 

It will thus be seen that the strength of shafts to resist 
torsion depends on four conditions : first, on the strength of 
the material ; second, on the diameter of the shaft ; third, 
on the length of the lever employed in twisting ; and fourth, 
upon the force or weight applied at the end of the lever. 

The following Table shows the values assigned in the fore- 
going remarks as the ultimate strength of a bar 1 inch in 
diameter, the weight being applied to a lever 12 inches 
long. 





TABLE 


XXXII. 




Cast steel 


rHigh 
J Ordinary. 
1 Mild 
I Bessemer. 




1,900 lbs 
I »5°° 5, 
i,355 „ 
1,150 „ 


Wrought iron 
Cast iron 
Wrought copper 






700 to 1,000 „ 

650 to 750 ,, 

. 400 to 450 , , 



The following Table conveys some precise knowledge in 
regard to torsion : — 



138 



On tlw Strength of Materials. 





fc 




e 


1— 1 






^ 




•is 


X 




X 


^ 


x • 


-8 


H 


* 


•-1 




PQ 


fc 


< 




H 


5S 



ns 3 c bo o 



'53 <y — 



= ^. 



^5> 



o > »y 

SSI ^ 

!? g « w 



§1 

S3 

<u — ; 

IP'S o 

§£ e 
5 ■•- 



11 

s 

— 



Resistance to Torsion and Shearing. 139 

Table collected from various sources, showing the re- 
lative strength of metals to resist torsion, wrought iron 
being 1. — 

TABLE XXXIV. 

Wrought iron ....... I - oo 

Cast iron ........ -90 

Cast steel 1-95 

Gun-metal ....... -50 

Brass ........ -46 

Copper -43 

Tin ......... -14 

Lead -io 

The above relative values must be considered as approxi- 
mate only, because the resistance of different specimens of 
the same material varies more or less, according to its 
quality. 

A few examples of the strength of crane shafts will be 
given, in the Chapter on Complex Structures. The nature of 
the stress to which such shafts are subjected is more like 
that which is produced in experiments, on the absolute 
strength to resist torsion, than is the case in mill work, where 
strength and stiffness become complicated with the question 
of motion and velocity. The strength of a shaft required to 
transmit power depends entirely upon the speed at which 
it is driven ; a shaft that will convey 10 horse-power at 
a velocity of 50 revolutions per minute, will be strong enough 
for 30 horse-power at 150 revolutions, and so on in propor- 
tion. 

Example. — To find the horse-power that can be trans- 
mitted by a good wrought-iron shaft, 3 inches diameter, 
driven by a wheel 2 feet in diameter, at a speed of 150 
revolutions per minute. From the Table, we find that a 
1 -inch shaft will break with a stress of 800 lbs. acting at 
the end of a 12-inch lever, or at the pitch-line of a wheel 
2 feet in diameter, and as the strength increases as the cube 



140 On the Strength of Materials. 

of the diameter, a 3-inch shaft will break with 21,600 lbs. 
acting at the periphery of the driving wheel. 

Let it be assumed that we are not to strain the shaft to 
above -|th of the breaking-weight, then we may have a con- 
stant load of ^J-jp-&= 3,600 lbs. acting upon the wheel. 

The wheel, in making one revolution, travels over 2 
x 3*i4i6=6'28 feet, and in running one minute 6*28 x 150 
=942 feet. 

Then the number of foot-pounds that can be transmitted 
by the shaft will be the load of 3,600 lbs. multiplied by the 
distance through which it travels — namely, 942 feet ; thus, 
3,600 x 942=3,391,200, and this number divided by 33,000 
= 10276, which is the number of actual horses-power that 
can be transmitted by the shaft, under the given conditions 
of speed and factor of safety. 

In the foregoing example, it is assumed that the load upon 
the driving-wheel is constant, which is true for ordinary shafts, 
but, in the case of an engine crank-shaft, such a condition 
cannot hold, because, even when the pressure on the piston 
is uniform, there are some points in the revolution at which 
the twisting force is practically equal to the full load upon 
the piston, while at other points the twisting force is nil, 
although of course the horse-power exerted by the piston 
and crank are equal. 

The average pressure upon the crank is equal to the 
pressure on the piston, multiplied by the distance which it 
travels in making a double stroke, divided by the distance 
through which the crank-pin travels in the same time ; now, 
the piston passes through a distance equal to twice the 
diameter of the circle described by the crank-pin, whereas the 
crank-pin travels over a distance equal to 3*1416 times that 
diameter, and hence the mean strain on the piston equals 
~-4- L§==I '57 times the driving pressure upon the crank. 

The varying strain thrown upon the crank-shaft is made, 
approximately, uniform by the fly-wheel, and hence second 



Resistance to Torsion and Shearing. 141 

motion shafts may be said to be uniformly loaded through- 
out, but it is evident that the portion of the crank-shaft, 
between the crank and the fly-wheel, has to withstand a 
greater strain than the. part on the other side of the fly- 
wheel, in the ratio of 1*57 to 1, and it has to be made stronger 
to resist it. 

In the case of engines working expansively, the horse- 
power is governed by the mean pressure upon the piston, 
but the crank-shaft has to be of sufficient strength to with- 
stand the greatest pressure on the piston. 

For example, if we had an engine working with the full 
pressure of steam during the whole of the stroke, and an- 
other of precisely equal power working with the same steam 
pressure at the commencement of the stroke, but cut off at 
\ of the stroke, the mean pressure on the piston of the latter 
engine would be '846 of that upon the other piston ; and 
hence to enable them both to perform the same amount of 
work, the area of the piston of the latter would have to be 
1 "i8 times greater than that of the former, and the maximum 
strain on the crank-pin and crank- shaft of the expansive 
engine would be ri8 times that upon the crank-pin and 
shaft of the other engine, although the horse-power trans- 
mitted through the two shafts is precisely equal in each 
case. 

It is necessary, therefore, in ascertaining the proper size 
for a crank-shaft, to hnd first the maximum pressure brought 
to bear upon the shaft, then multiply that pressure by the 
number of times the breaking strength is to exceed the 
working strength, and find the size of shaft, as explained for 
the ordinary shaft. 

Example. — Required the diameter of the crank-shaft for a 
horizontal engine, which is to be worked with a pressure of 
45 lbs. per square inch throughout the stroke, the diameter 
of the cylinder being 36 inches, and the stroke 5 feet, and 
the breaking-strength to be six times the working-load. 

1. The maximum pressure on the crank-pin, exclusive of 



142 On the Strength of Materials. 

friction, will be the pressure per square inch upon the piston 
multiplied by its area, thus, 45 x 36* x 7854=45,804 lbs. 

2. The breaking-strength =45,804 x 6=274,824 lbs. The 
leverage at which this maximum pressure acts is 4=2^- feet, 
and the weight required to break a i-inch bar when acting 
at the end of a 2^-feet lever = |?4> = 320 lbs. ; but we have 
to provide for a weight of 274,824 lbs., and hence we must 
have 2 - j y^- 4 =859 times the resisting power of a i-inch bar, 
and as the strength varies as the cube of the diameter, the 
cube-root of 859, which is equal to 9*5, will be the diameter 
in inches of shaft required. 

To take another example. Let it be required to find the 
diameter of the crank-shaft, for an engine equal in power to 
that in the previous example, worked at the same pressure 
at the commencement of the stroke, but with the steam cut 
off at half stroke, the length of stroke of the piston being 
equal in both cases. 

It has been shown that the area of the piston, and hence 
the maximum pressure upon the crank, would be 1*18 times 
greater than in the former engine ; therefore we must provide 
for 274,824 x 1*18=324,292 lbs. acting on the same leverage, 
and the diameter of the shaft required will be the cube-root 
of 32 3 4 o 2 o 92 ? which is equal very nearly to 10J inches. 

These few examples will serve to show that it is necessary 
to know something more than the horse-power of .an engine, 
before we can determine the proper size of the crank-shaft, 
for, although the horse-power is precisely the same in both 
engines, the one requires a shaft f ths of an inch larger in 
diameter than the other. 

In each of the foregoing examples, the shafts have been 
assumed to possess sufficient torsional stiffness, and they 
would do so in the case of the crank-shafts which are short, 
and the 3-inch shaft might be able to transmit the stated 
number of horse-power, but it might twist through so many 
degrees that it would be quite unserviceable for driving 
machinery. There are likewise other points to be looked 



Resistance to Torsion and Shearing. 143 



at, beside the horse-power to be transmitted, even with 
ordinary shafting, namely, the distance from the driven end 
of the shaft to the point at which the power is taken off, for 
a shaft might be quite strong and stiff enough to drive 
certain machinery, provided the power was taken off near 
the driver, but the case would be widely different if the same 
power were taken off the shaft, say at 300 feet, instead of at 
a comparatively short distance from the driver. 

The torsional stiffness of wrought-iron shafts varies as the 
fourth power of their diameter divided by the length, and it 
is found that wrought-iron shafts above 4^- inches diameter, 
which are strong enough to resist the torsional strain, will 
be found sufficiently stiff to do their work ; but below that 
diameter the stiffness of the shaft is the weak point, hence 
deflection must be otherwise provided for, in order to afford 
the necessary strength ; therefore, a shaft of larger diameter 
than is absolutely necessary to resist the torsional strain 
must be used, in order that it may be sufficiently stiff for 
the steady driving of the machinery, so that in determining 
the proper size to be given to a long line of shafting, all 
these important points should be taken into account. 

Resistance to Shearing and Punching. 

The resistance of materials to the action of shearing and 
punching has not yet received so much attention as some of 
the other more important modes of resistance. Still, suffi- 
cient is known of the amount of force necessary to shear or 
punch wrought iron, to enable the student to form an ap- 
proximate estimate from their relative tenacity, of the shear- 
ing and punching resistance of other metals, which have not 
yet been operated upon to the same extent. 

The force which is required to shear or punch, depends 
on two conditions : first, upon the extent of surface which is 
to be shorn or broken through ; and secondly, upon the 
nature or kind of material that has to be operated upon. 



144- On the Strength of Materials. 

The operation of shearing or punching is not strictly a 
cutting, but a detruding action, and the whole work is done 
almost at the commencement or immediately after the first 
yielding. That some time is occupied in shearing or 
punching is largely due to the inherent elasticity of the 
material, the punch, and the machine, but when the elas- 
ticity and slackness are used up, then the resistance offered 
by the material is at once overcome, and the metal is de- 
truded, broken, or pushed off, rather than cut through, and 
when the operation is performed, the resilience of the appa- 
ratus in assuming normal conditions is accomplished with a 
jerk. 

From this it will naturally be inferred, that the process 
of shearing and punching requires a greater immediate 
mechanical force to accomplish the object, in that way, than 
would be required to cut the portion with an incisive instru- 
ment by a more gradual cutting or perforation. There is, 
therefore, from such an action, a constant repetition of 
sudden strains coming upon the tools, which, although last- 
ing only for a second, yet when united in effect, tend to 
rupture the apparatus, unless it is made exceedingly strong, 
and this accounts for the ultimate breakage which generally 
overtakes all such machines, and which is fully explained by 
the results, shown in the Tables, relating to the elasticity of 
cast iron. 

The resistance that is offered to shearing is a fraction 
under that of punching, and both are found to be a little less 
than the tensile strength of a piece of the material of equal 
area ; and from some experiments made on shearing and 
punching wrought iron, it appeared that, with fair uniform 
bearing instruments, to punch a hole one inch diameter in 
an inch plate, or to shear through a bar three inches broad 
by one inch in thickness, required nearly 80 tons of stress, 
the stress being as the metallic surface disturbed or broken 
through, which in these two cases would be nearly the same. 
With a half-inch plate or a bar half an inch thick, the stress 



Resistance to Torsion and Shearing. 145 

would be about the half of 80 tons, and so on in propor- 
tion. 

This amount of stress is considerably higher than that 
which appears to have been obtained, in some other pub- 
lished experiments, which go to show that the force re- 
quired to shear or punch is about 80 per cent, of the tensile 
strain. But in making such experiments, however care- 
fully, the result will much depend upon the precise condi- 
tion of the acting surfaces of the punch or shears ; for unless 
these surfaces have a perfectly flat and fair bearing, at the 
commencement of contact of, the instruments, the work of 
the shearing or punching will be performed in detail, and 
thus the apparent strain will be reduced by being spread 
over a longer time. Hence arises the great practical advan- 
tage which is found to result from making the face of such 
punches so as not to have a fair bearing at the commence- 
ment, but slightly out of parallel with the bolster, and like- 
wise the arrangement of the shears so as -to act like a pair 
of common scissors, which give a gradual shear. 

When it is said that the resistance to a shearing action is 
nearly the same as the resistance to tensile strain, it has to 
be borne in mind that the effect will depend on various 
conditions, for there are many forms of construction which 
may and do call the shearing action into activity, un- 
intentionally, from some modification of the mechanical 
arrangements ; to take, for example, the case of long links, 
in which the connection is formed by means of an eye or 
hole at the ends, into which a pin or bolt is inserted. 
It might be inferred that the bolt should have the same 
sectional area as the body of the link ; but it is found that 
when so made, the round pin acts as a blunt wedge within 
the hole, and thus tends to tear it open. To give uniformity 
of strength, it is found necessary to provide a larger bearing 
surface, in order to counteract this detrusive tendency, and 
it is for this reason that some engineers have the bolts or 
pins of such structures, apparently out of proportion, gene- 



146 On the Strength of Materials. 

rally to the extent of half a diameter, but this is true 
economy, notwithstanding. 

The practical question is frequently raised, in regard to 
the comparative merits of punching and drilling, in per- 
forating the rivet holes in boiler plates and for similar 
purposes. Punching is the cheaper process, and has the 
advantage of finding out and breaking an exceptionally 
bad or brittle plate, but, on the whole, it is not so effi- 
cient as drilling. The drill, being a cutting instrument, 
deals more gently with the material, and the plate, so treated, 
is more likely to maintain its full strength after the opera- 
tion. As the line of rivets is the weakest part of the 
structure, it seems throwing away an important advantage 
not to drill the holes, even if it is a little more expensive to 
do so. It is probable, however, that if the drilling system 
were established, by proper organisation of plant and well- 
directed arrangements, it would not be a more costly process 
than punching. Already some of the larger engineering 
houses are drilling their boiler plates, and are able to make 
boilers almost as economically, on that system, as by the 
older plan of punching. 

From some valuable experiments made in 1858, which 
are recorded in the Proceedings of the Institute of Me- 
chanical Engineers, and were published in the ' Artizan ' of 
that year, it was found that the stress required to punch a 
hole one inch in diameter, through a wrought-iron plate \ 
an inch in thickness, was equal to 36 tons, and to force 
the same punch through a plate of double the thickness 
required 69 tons, which is not quite the double of the 
former result. The mean of the two experiments gives 
22*5 tons, per square inch of detruded sectional area. 

A punch 2 inches in diameter was, pushed through three 
plates in succession, the respective thicknesses being \ an 
inch, 1 inch, and \\ inch, and the varying pressures required 
were 65, 132, and 186 tons. This gives a lower mean than 
the former — namely, 19*4 tons per square inch of detruded 



Resistance to Torsion and Shearing. 147 

sectional area — thus showing that, by increasing the size, 
the proportionate stress diminishes, as in the above ex- 
amples, to the extent of 14 per cent. 

The following Table contains the results of another set of 
experiments, made with actual weight on the end of a lever, 
the weight being gradually applied, until the iron was de- 
truded : — 



TABLE XXXV. 



Diameter of 
punch. 

Inch. 


Thickness of 

wrought-iron 

plate. 

Inch. 


Sectional area 
of detrusion. 

Square inches. 


Total weight 

bearing 

on punch. 

Tons. 


Stress per 

square inch 

of area. 

Tons. 


0-250 
0-500 
0-750 
0-875 

i-ooo 


0'437 
0-625 
0-625 
0-875 

i-ooo 


0-344 
0-982 
1-472 
2-405 
3-1416 


8-384 
26-678 
34768 
55-000 
77-I70 


24-4 
27-2 

23-6 
23-1 
24-6 



In the several experiments, the average pressure required 
for punching seems to be greater for thin plates than for 
thick plates, which is probably due to the greater relative 
proportion of hard exterior surface in the thinner plates. 

From a comparison of experiments, in punching and 
shearing, the stress required to detrude, per unit of sec- 
tional area, appears to be nearly the same in both cases, 
with moderately small holes ; but with large holes there is a 
perceptible difference, nearly 5 per cent, less pressure being 
required to shear than to punch a given sectional area, which 
is probably owing to the effect of friction at the entrance of 
the punch. 

For comparison, the following Table, taken from the 
Proceedings of the Institute of Mechanical Engineers, will 
show the stress required for shearing : — 



148 



On the Strength of Materials. 



TABLE XXXVI. 





Sectional area 


of surface 


Pressure on the detruding 




Direction 


detruded. 


instrument. 












of shear. 








Stress per 


Remarks. 




Thickness and 


Area in 


Total pres- 


square inch 






breadth in 


square 


of area de- 






inches. 


inches. 




truded in 
tons. 














Mean stress. 


flat 


0*50 x 3-00 


I'50 


33*4 


22-3 


j-227 


edge 


0*50 x 3-00 


I'50 


34*6 


2 3 -I 


flat 


i*oo x 3-00 


3 -00 


69-2 


23-1 


] 


edge 


i-oo x 3-00 


3 -00 


68-i 


227 


|2I-5 


flat 


I'OO x 3*02 


3-02 


597 


19-8 


edge 


i-oo x 3*02 


3-02 


62-1 


20 -6 


J 


edge 


i-8o x 5-00 


I0-20 


210-6 


20-6 





The. foregoing experiments were made with the shearing 
instruments parallel, when the work of detrusion was done 
after the first pinch. It was found that by spreading the 
operation over a longer period by means of inclined instru- 
ments, the stress required was considerably reduced, as will 
be seen by the following Table : — 



TABLE XXXVII. 





Stress with bar 


Stress with bar 


Percentage of 


Size of bar in inches. 


laid flat upon its 
side, in tons per 


laid on edge, in 
tons per square 


less stress required 
when detruded on 




square inch. 


inch. 


flat surface. 


3 x \\ 


18-2 


20'I 


IO 


4i x if 


I4-3 


I7-9 


20 


3 x 1 


157 


2IT 


26 


si x i-i 


167 


22*6 


26 


6 x il 


I5-0 


l8"4 


18 



The above experiments were made with shears, the blades 
of which were at an inclination of 1 in 8. The less stress 
required when the same bar of iron is cut on the side, is 



Uniformity of Sectional A re a. 



149 



most probably due to the circumstance that the work to be 
done is spread over a longer period. 

By comparing the stress per square inch in Table XXXVII. 
with that in Table XXXVI., we obtain the averages given 
in the following summary of results : — 



Description of 
shearing blades. 


Mean force required to 

shear bars on fiat, in tons 

per square inch. 


Mean force required to 
shear bars on edge, in 
tons per square inch. 


Parallel 
Inclined 


217 
16 


217 
20 



Thus teaching four important lessons. First, that with 
parallel shears, the shearing force required is equal in either 
position of the bar. Second, that with inclined shears, the 
shearing force is 20 per cent, less for the bars on the flat, 
than it is for the same bars on edge. Third, that when the 
bars are cut when placed on edge, only 8 per cent, is saved 
by using inclined shears. Fourth, that when bars are 
sheared on the flat, a saving of 26 per cent, is effected by 
the inclined, as compared with the parallel shears. 



CHAPTER XL 

ON THE IMPORTANCE OF UNIFORMITY OF SECTIONAL 
AREA. 

In designing machines or structures, not only is there a 
correct form, but it is of the greatest importance, that that 
form should not be departed from unnecessarily. The 
correct form is that, in which every part is proportioned to 
the straining action to which it is subjected, so that the stress 
reaches the same maximum limit on every section. If, in- 
stead of being thus proportioned, a structure has a surplus 



150 On the Strength of Materials. 

of material in some parts, that surplus may not only not 
strengthen it, but may positively weaken it, and may render 
parts, otherwise of sufficient strength, incapable of sustaining 
the load for which they have been calculated. Thus, for 
example, a chain with one link smaller than the others, a 
shaft with one journal of insufficient diameter, or a tie-rod 
nicked at any point, is reduced in strength, not only in pro- 
portion to the reduction of section at the weak point, but in 
a still greater degree. In consequence of the surplus re- 
sistance in the other parts, most of the elastic work will be 
concentrated on the weak link, the weak journal, or the 
nicked section of the tie, as the case may be, and those 
parts will gradually be more weakened, and at last over- 
come, before the other parts of the structure are affected. 

Even before the principle just indicated was fully under- 
stood, it was more or less anticipated by experienced 
engineers ; and it is interesting to recall the intuitive skill in 
construction, often displayed in the forms adopted for the 
details of structures. For example, in parts of early loco- 
motive engines, where cotter holes or keyways were formed, 
an increased depth or thickness was generally given at that 
point, so as to make up for the material cut away. By this 
means the whole structure was brought approximately to 
equality of resistance, and the concentration of the elastic 
work on a particular section was prevented. 

Although, strictly speaking, we cannot increase the 
strength of a structure by securing equality of sectional area, 
because the strength still remains dependent on the weakest 
section, yet virtually we increase the strength, by preventing 
the gradual deterioration of the resistance at one point, and 
thus diminishing the risk of fracture. 

As a simple example, let us consider an ordinary screw 
bolt. A screw bolt may be formed, either with the screw 
thread in relief, the shank being of the same diameter as the 
screwed part at the bottom of the threads, or the screw may 
be cut into a bar, and the shank is then of the diameter of 



Uniformity of Sectional A rea. 151 

the screwed part, measured to the outsido of the threads. 
Two bolts may be thus formed, of the same section at the 
weakest part, but the former bolt will yield equally through- 
out when loaded, while the latter will yield chiefly at the 
point of junction of the screw thread with the shank. Hence, 
when subjected to stress, the stretching will be distributed 
in the former, but in the latter the screw threads will be 
drawn out of pitch, and will no longer match the nut. If 
these two bolts are treated alike, say by using a screw key 
w T ith a long handle, so as to twist off the nut by tension, or 
by combined tension and torsion, then the former bolt, 
although lighter in weight, will yet require more turns of the 
screw key before it will give way than the latter. Practically 
it is the stronger, and it is important that this should be 
understood, because the same principle is applicable in 
many other cases. 

It is not essential that the screw thread should be in relief, 
with a small shank, the uniformity of sectional area may be 
maintained in other ways. For many purposes it is con- 
venient that the shank of the bolt should fit the bolt hole, 
and the bolt hole must be large enough to admit the screwed 
part Hence, in these cases, the shank of the bolt requires 
to be maintained equal in diameter to the outside diameter 
of the screw thread. To secure uniform section in the bolt, 
various plans have been adopted. In some bolts, the shank 
is made hollow from the head up to the neighbourhood of the 
screw thread. These bolts have been used in fixing armour 
plates. In other bolts, the shank has been made of cruci- 
form section, or of a square or triangular section with 
rounded corners. All these plans give satisfactory results, 
so far as depends on the uniformity of the section. 

The condition of uniformity of section, in practical opera- 
tions, is liable to be modified, either for the better or the 
worse, in many ways. For example, the effect produced in 
the forming of the screw thread of bolts such as those be- 
fore referred to, may be seriously injured unintentionally,, 



152 On the Strength of Materials, 

from the mode of making, cutting, or forming the thread, as 
depending on the sharpness or bluntness of the screwing 
dies. With good instruments, which do really cut out the 
thread, and do not distress the internal structure of the 
material, the bolts are more reliable than those that are 
formed with blunt dies, which act more as abrasive, or even 
detrusive instruments, than as genuine cutters. The effect 
of such violence of treatment is to harden or loosen the iron, 
and to render the bolt more brittle. With good instruments 
and ordinary care in the manufacture, and when the form of 
bolt section has been arranged on correct principles, the 
strength of bolts is about equal to that of the iron out of 
which they are made, ranging between 20 and 25 tons per 
square inch of sectional area at the weakest point, according 
to quality. 

Similar remarks apply to the strength of chains. The dis- 
astrous effect of a weak link is seen, more especially, in those 
chains that are used for cranes and in slings for lifting heavy 
weights. As a rule, such chains are proved up to about the 
half of the ultimate tensile strength, or about the double of 
the intended ultimate working load, nevertheless it is fre- 
quently found that, after working for a short time, some 
weak link begins to stretch, and if this is not observed in 
time, it will break unexpectedly. Such a link must have been 
weak originally, and, during its working career, it must have 
had more than its fair share of the elastic duty to perform ; 
hence if it is not cut out of the chain in time, it will ultimately 
break with a considerably less load than that which it was 
intended to support, or less than the quarter of its original 
ultimate strength in its early days ; on the other hand, when 
a chain is so well made that all its links are of uniform 
strength, or nearly so, the endurance is much greater, and it 
will go on for an indefinite period without breaking. At 
the same time, a change for the worse overtakes all chains 
in course of time, that is, if they are in constant use; and, in 
consequence, it is a rule in the War Department, that all 



Uniformity of Sectional Area. 



153 



chains of cranes or slings are to be drawn through the fire, 
and thereby annealed, periodically, which has the effect of 
restoring the quality, by putting the material of the links 
into a condition of equilibrium. By this course, their life is 
protracted indefinitely. After the chains are annealed, they 
are then subjected to a proof strain, which is the half of the 
ultimate strength, and double the usual working load, ac- 
cording to size, which is as under : — 





TABLE XXXVIII. 






Table of Proof Strains. 




Size of iron in 
chain, 


_, r . Size of iron in 
Proof strain, 1 cha - m> 


Proof strain, 


in inches. 


in tons. j n inches. 


in tons. 


lil 


!§ 


13 
IS 


11 


3 

3 


If 


7 
8 


9\ 


7 
16 


2i 


15 
ICi 


i°i 


* 


3 


I 


12 


9 
16 


->3 
04 


If 


i5l 


5 

8 


4| 


T l 
X 4 


18} 


11 

10 


5l 


T 3 

X 8 


22f 


3 

4 


6| 


I* 


27 



Chains are of two sorts : first, the open link chain, which is 
commonly used for cranes and like purposes ; and second, 
the stayed link chain, which is used for cables and some other 
purposes. It is to be noted that, whatever the explanation 
may be, the stayed link, when made of the same iron as the 
open link, is stronger than the other, nearly in the proportion 
of 9 to 6. To take, for example, an inch chain, that is to 
say, a chain made with iron one inch in diameter, the ulti- 
mate strength of the open link is about 24 tons, while that 
of the stayed link may reach 30 tons. The office of the 
stay is to prevent the collapse of the link, and thereby to 
intercept the shearing action due to the wedge action of 



154 On the Strength of Materials. 

the one link within the other. The great practical objec- 
tion to the stayed link chain is its weight, and its extreme 
roughness in working over pulleys. 

A good approximate rule, for mentally estimating the 
strength of chains, is to remember the strength of one par- 
ticular size — say of one-inch chain — the safe working load 
of which is 6 tons for the open link, and 9 tons for the 
stayed link : the comparative strength of other chains is to 
that of the inch chain, as the squares of the diameters of 
the iron out of which they are severally made. This does 
not hold strictly correct with very large, nor with extremely 
small sizes, which both lose strength to a small extent, the 
former from the iron not being quite so good, and the latter 
from the welding not being quite so perfect. 

Another simple rule, for the approximate safe working 
load of chains of different sizes, is to square the number of 
eighths of an inch, in the diameter of the iron out of which 
the link is made, and to strike off the last figure as a 
•decimal. For example, in the inch-chain there are 8 
eighths of an inch. 

8 x 8 = 64, 
or, striking off the last figure, 6*4 tons, the greatest safe load. 

Again, for a -J inch chain, 3x3= 9. Striking off the last 
figure we get 0*9 tons for the greatest load consistent with 
safety. 

Uniform and proportional sectional area adds to the 
strength of beams, when subjected to transverse strains. 
Any notch made on the under side of a beam for the in- 
sertion of bolts, nuts, or washers, should be studiously 
avoided. 

In the construction of heavy timber roofs, where diagonal 
bolts or tie-rods have to be introduced, at an angle, through 
the principal beam, some persons are so unskilful as to make 
a notch on the under side of the beam, for the nut and washer. 
Such an arrangement is most objectionable, because the dam- 
age done to the strength is permanent. The proper course, 



Uniformity of Sectional A rea. 155 

under such circumstances, is to employ a broad iron washer- 
plate, with its flat surface bearing upon the under side of the 
beam, the washer-plate having a hole cored out, at the proper 
angle for the reception of the bolt, and with a corresponding 
boss, having the bearing surface for a nut and supplementary 
washer, at right angles to the axis of the tie-rod. 

Another objectionable practice sometimes seen, in con- 
nection with rough structures, is the formation of slits or 
cotter- ways in bolts, and in having that part of the bolt made 
with the same exterior diameter as the solid portion of the 
main body. Such a bolt would be really stronger, for all 
practical purposes, if the main body was reduced to a smaller 
diameter, equal in sectional area to the part in which the slit 
has been made. The proper course is, to upset the bolt at 
the part which has to be punched, and then to form the 
cotter-way by taper punching, in order to leave the metal 
entire, and thus obtain uniformity of sectional area. 

The Strength of Ropes. 

The strength of hempen ropes is found to depend 
primarily on the quality of the hemp fibre with which they 
are made. The fibres vary from 3 to 3 \ feet in length, and 
a number of them are twisted together to form a yarn, this 
twisting introduces the element of friction, which effectually 
prevents the fibre from being drawn asunder. When a rope 
is twisted it necessarily becomes shorter than the strands 
of which it is made, and the amount of twist given to ropes 
is usually expressed by the extent to which they are short- 
ened ; thus if shortened one quarter of their length, the twist 
is then said to be one quarter. The nom,inal size of ropes 
refers to the circumference, thus a six- inch rope is a rope 
of six inches circumference. 

As a rule, new white ropes are stronger and more pliable 
than ropes made with tar. The tarred rope, however, retains 
its original strength for a longer period, especially when ex- 



156 On the Strength of Materials. 

posed to wet. Tarred ropes spun hot are stronger than 
tarred ropes spun cold, and are more impervious to water. 

The ultimate strength of ropes is usually considered to be 
about 6400 lbs. per square inch of sectional area. From 
some recent experiments made at Woolwich, the strength 
was found to range from 9874 lbs. in a 9-inch to 10,783 lbs. 
in a 2-inch rope. The same series of experiments showed 
that Italian hemp ropes are stronger than those of Russian 
hemp. 

The Woolwich experiments teach also three important les- 
sons to the student : — 1st. That there is much variation in 
the strength of pieces of rope even when cut from the same 
coil. Thus, the 4-inch ropes range in tenacity from 5! to 
7 Jf tons. The 6-inch ropes from 14 J to 17 tons. The 
9-inch ropes from 25 to 29J-J- tons. The minimum strength 
observed in the experiments is that which should be relied 
on in practical calculations. 2nd. That there is consider- 
able loss of strength from the tear, wear, and exposure to 
the weather during a few months working. Thus the 
strength of an apparently good 6-inch Italian hemp rope, 
after working, was only iof tons, as compared with 14^ tons, 
the strength o*f a new rope. The old 6-inch Russian hemp 
rope broke with 5^-, while the new one required n \ tons. 
This fact suggests that we ought to allow a large margin be- 
tween the working safe load and the ultimate strength of 
new ropes. Thus, we may make the safe load Jth of the 
ultimate strength. 3rd. That a double rope is in certain 
cases weaker than would be expected from experiments with 
single ropes. All the double rope slings, suspended from 
an ordinary crane hook, broke with less than double the 
strength of a single rope. On the other hand, when thimbles 
or pulleys were used, then the double ropes nearly always 
required double the maximum load which would break a 
single rope. 



PART II. 

ON THE STRENGTH OF STRUCTURES. 



CHAPTER XII. 

BEAMS AND GIRDERS. 

Having described the physical properties of the various 
materials employed by the engineer, we have next to con- 
sider those structures, either simple or complex, the strength 
of which depends on the form, arrangement and construc- 
tion, of the parts, as well as on the material of which they 
are composed. 

In studying the laws of the resistance of structures, a 
knowledge of elementary mathematics is necessary. In the 
following chapters, the subject is treated in the most simple 
manner, in the hope that they may thus be rendered useful 
to all classes of readers, and especially to those whose 
mathematical knowledge is limited, by enabling them to 
calculate the strains in the more simple structures required 
in practical operations. 

Every practical engineer should be able to ascertain, 
approximately, the strains which are likely to be brought 
upon the component parts of any structure, both by the 
weight of the structure itself, and the load which it is 
intended to support. He should likewise know the amount 
of stress which may, with perfect safety, be put upon each 
square inch of section of the material of which the structure 
is composed. It will then become a matter of simple pro- 



158 On the Strength of Structures. 

portion, to ascertain the number of square inches of any- 
given material, that should be introduced into each part of 
the structure, in order to enable it to resist with safety the 
strain which it will be required to sustain. 

Of late years, unfortunately, too much reliance has been 
frequently placed upon the formulae which are to be found 
in different books ; these are drawn from a variety of sources, 
and are generally given without the data from which they were 
originally deduced. This reliance upon mere formulas is a 
great mistake, and often leads to expensive errors. In some 
cases, formulae, originally intended for one kind of structure, 
have been applied in designing a different kind of structure, 
and the incorrect result arrived at has only been discovered, 
when too late to avoid the consequences of the mistake. 

In the following chapters, the natural laws of mechanics 
are brought into prominence, so that the student may be 
led to use his judgment in the application of rules. At the 
same time, a general knowledge of mathematics will be 
found of the greatest value, giving a more comprehensive 
grasp of the whole subject, and fitting the student to use 
formulae with intelligence. 

From a very early period, it was known that the rectan- 
gular beam, placed on its edge, would carry safely a heavier 
vertical load than the same beam placed upon its side. In 
the same way, it was understood that a given quantity of 
material, arranged in a hollow form, was stronger than when 
in the solid shape. The reasons why these things are so, 
are now also well understood, and the practical engineer 
should make himself acquainted with them, if he would 
carry out works with safety and economy. 

The present chapter will relate chiefly to beams and 
girders, and the principles applicable to these are mostly 
derived from the investigations and experiments of Hodgkin- 
son, Fairbairn, and others. An effort has been made to 
explain these principles in as simple a manner as possible ; 
but the full treatment of the subject would involve a higher 



Beams and Girders. 159 

degree of mathematical knowledge than is here assumed. 
The student who wishes to pursue the subject further is 
recommended to consult the treatise by Professor Twisden, 
in the same series as the present volume. 

Beams or Girders. 

The term 'beam' is generally applied to any large piece 
of material, which carries a load at a distance from the 
point or points of support upon which it rests, and which is 
thereby subjected to transverse strain. But this term, con- 
joined to another word, is often used for certain parts of 
structures, which in reality are subjected to longitudinal 
strains only, such as, for instance, 'tie-beam' or 'straining- 
beam,' both of which are subjected to tensile strains only. 

The term ' girder ' is now almost universally adopted by 
engineers, as the name for beams, which are supported at 
both ends and subjected to transverse strain, and the term 
' cantilever' is generally used for beams, which are supported 
at one end only and subjected to transverse strain. 

Girders are made of many forms, depending on the 
material employed. Those in most common use are of the 
rectangular, flanged, or tubular forms of section ; the flanged 
girder is indiscriminately made of cast, or wrought iron, 
and the term includes all forms in which a flange or flanges 
are connected to a single vertical web, whether the web is 
a solid plate or an open lattice, or whether the flanges are 
parallel or otherwise. 

In tubular girders, which are mostly built up of wrought 
iron, the two flanges are connected by two webs, and in the 
case of the celebrated tubular bridges of Fairbairn, the 
tubular girders are of such large dimensions, as to admit of 
the load being carried inside the tube, instead of on the 
outside in the usual manner. 

In considering the strength of beams or girders, when 
subjected to transverse or cross strains, three chief points 
present themselves for consideration, namely : — 



160 On. the Strength of Strnctzires. 

First, the mechanical effect which any given load pro- 
duces upon the section of fracture, of whatever form, under 
varying conditions of support. 

Second, the nature of the strains that are brought to bear 
upon the girder, and the manner in which its resistance to 
those strains is affected by the form of the section of the 
girder. 

Third, the actual strength of the material composing the 
girder, which is to be thus strained, and which can only be 
determined by direct experiment, or by placing reliance on 
the numerous published experiments, which have been so 
carefully carried out, by Barlow, Fairbairn, Hodgkinson, 
Kircaldy, and many others. 

The relative strength of a girder, so far as it depends on 
the manner in which it is loaded and supported, can be ex- 
pressed very simply. Taking a given girder, of a given span, 
the load may vary in the ratio of i to 8, according to the 
different ways in which the girder is supported and the load 
distributed. 

Position of Support and Load. 

Relative 
strength. 
When supported at one end and loaded at the other . . i 

When supported at one end and load distributed . . 2 

When supported at both ends and loaded at the centre . 4 

And when supported at both ends and the load equally 

distributed 8 

When a uniform beam is securely fixed at both ends, by 
encastrement or otherwise, instead of merely resting on sup- 
ports, it is then under an entirely different set of conditions. 
Theoretically it would break, simultaneously, at three diffe- 
rent sections, instead of giving way in the middle only, but 
practically this would never occur, unless the fixing of the 
ends were exceedingly firm, as, for instance, when the beam 
and the abutments were part of the same casting. The in- 
crease of strength, due to secure fixing of the ends, has been 
variously stated ; according to some, the relative strength of 



Beams and Girders. 161 

the beam above referred to would become equal to 12, and, 
according to others, even to 16 ; but it is obvious that the 
value will depend on so many conditions, that it is impossible 
to say precisely what it is, beforehand ; it must, therefore, be 
considered as doubtful, unless all the conditions are known 
definitely : at the same time the importance of secure fixing, 
wherever it can be employed should be noted. 

The reason why the same girder possesses the above rela- 
tive strengths, under the given varying conditions, may be 
very clearly shown, by supposing the girder in question to 
act as a bent lever, one arm of the said lever being equal in 
length to the distance from the point of support to the weight, 
and the other arm of the lever to be the depth of the girder. 

In considering the strength of such a girder, in which the 
amount of deflection due to the load is inconsiderable, we 
may neglect the small curvature of the beam when loaded, 
and consider that the straining forces act perpendicularly to 
the longitudinal axis of the beam. They are at right angles 
to the fibres of which it is composed, if it is a timber beam, 
and at right angles to the fibres, of which we may imagine it 
to consist, for theoretical purposes, if it is a metal beam. But 
the longitudinal tensions and compressions in the beam act 
parallel to the axis, or in the direction of the fibres of which 
it consists or may be imagined to consist. The loading forces 
act at right angles, therefore, to these tensions and thrusts. 

Let figs. 16, 17, 18, 19 represent four similar flanged- 
girders supported and loaded under the above-stated con- 
ditions. We know, by experience, that a weight acting at 
the end of a cantilever, as shown in fig. 16, will tend to bend 
the free end of the girder in a downward direction, as shown 
by the dotted lines a, b, c y which represent a bent lever ; 
we also know that, in order that such a lever may be in 
equilibrium, the product of the weight at the end of one 
arm, multiplied by the length of the arm, must be equal to 
the product of the length of the other arm, multiplied by the 
weight acting upon it. 



1 62 



On the Strength of Structures. 



Supposing, as an example, that a weight of i ton is re- 
quired at the free end of the girder to break it, and that the 



Fig. 16. 




girder is 4 feet long and 1 foot deep, then the weight or 
force, required at the other end of the lever, will be the pro- 
duct of the weight of 1 ton, multiplied by 4 feet, the length 
of the long arm of the lever, and divided by 1 foot the 
length of the other arm, and will be equal to 4 tons. 

The same girder (fig. 17), supported in a similar manner, 
but with a distributed load, will break with a weight of two 

Fig. 17. 




tons, or twice the weight required to break the first girder, 
because the mean distance at which the weight acts upon 
the beam, or, in other words, the centre of gravity of the 
weight will be only \ the distance from the support that it is 
in the former example, and hence it will have a leverage of 
2 feet instead of 4 feet. 
The breaking strain, or the force required at the end of 



Beams and Girders. 



163 



the short arm of the lever, is of course the same as in the 
first example- — namely, 4 tons — and the weight at the end of 
the long arm, necessary to produce the strain of 4 tons, will 
be 4 multiplied by 1 and divided by 2, that is 2 tons, 
or twice the weight required to produce the same strain 
when placed at the end of the cantilever. 

A similar girder (fig. 18), supported at both ends and 
loaded at the centre, will require 4 tons to break it, or 4 

Fig. 18. 




times the load required to break the first beam. The weight 
upon a girder, supported at both ends, is transmitted with 
undiminished force to its supports, and each support will re- 
act upon the girder with a force equal to a certain portion of 
the total load, according to the position of the weight rela- 
tively to the supports. 

The amount of each reaction is determined by the prin- 
ciple of the lever ; the reaction of either support bears 
exactly the same proportion to the total weight, that the dis- 
tance from the weight to the opposite support bears to the 
total distance between the supports ; for example, if we sup- 
pose a weight of 4 tons to act upon this girder, at a distance 
of 1 foot from one support, the distance to the opposite sup- 
port will be I of the whole distance between the supports, 
and the weight upon the near support will be f of the total 
weight, or 3 tons. 

When the weight is at the centre of the girder, as shown in 
fig. 18, the distance from the weight to either support is \ 



1 64 



On the Strength of Structures. 



the total distance between the supports, and hence the up- 
ward reaction of either support is equal to \ the total weight 
upon the girder. 

The leverage of each of these reactions is equal to \ the 
span of the girder, or 2 feet, and the force required to break 
the girder, when acting at the short end of the short ami of 
the same, is 4 tons as before, and therefore the reaction of 
each support must be 4 multiplied by 1 and divided by 2, 
which equals 2 tons ; and the total weight required upon 
the girder to produce the reaction of 2 tons upon each sup- 
port is 2 x 2 = 4 tons, and hence, the girder will not 
break, until it is loaded with 4 times the weight which would 
break the same girder, when supported and loaded as shown 
in fig. 16. 

The same girder, loaded with an uniformly distributed 
weight, and supported at each end, as in fig. 19, would break 



Fig. 19. 



OOCDOOOCDOO 



A, 




with eight times the weight required to break it, if supported 
and loaded as in fig. 16, or twice the weight which would 
break it if supported and loaded as in fig. 18. 

With an uniformly distributed load, each particle of the 
load acts with a gradually increasing leverage from the sup- 
port, where it is nil, to the centre, at which point it is equal 
to \ the length of the girder, and the mean leverage of all 
the particles composing the weight upon each half of the 



Beams and Girders. 165 

girder is at a point midway between the centre of the girder 
and the support. Its effect upon the material at the centre 
of the girder is precisely the same, as if half the weight upon 
each half of the girder was placed at a point twice the dis- 
tance from the support, which would be at the centre of the 
girder ; or, to state the result shortly, an uniformly distributed 
load has the same effect at the centre of the girder as half 
the same load acting at the centre. An uniformly loaded 
girder will not break until it is loaded with twice the weight 
which would break it, when placed at the centre of its length. 

The above has reference only to the theoretical conditions 
of beams, and does not take into account the weight of the 
beam. In the application and use of beams, practically, 
the weight of the beam itself must be considered. In small 
beams, of short span, the weight of the beam itself is small 
compared with the load it will carry. But in large beams, 
of long span, the weight of the beam itself becomes a very 
important element in the calculation. In long cast-iron 
beams, the weight of the beam itself may be equal to half 
the load it will carry, exclusive of its own weight. 

The strength of a beam is likewise affected, by the manner 
in which the materials of which it consists are disposed in 
its construction. Many theories have been propounded 
by eminent mathematicians, but scarcely any of these 
theories fully explains the law which gives the results found 
by experiment. The knowledge derived from experiment 
is, as a rule, quite sufficient for the greater number of con- 
structions in ordinary practice, and on this the following 
observations depend. 

We have already seen that the girder tends to bend under 
its load, and hence the top layer of fibres must necessarily 
be compressed, and the bottom layer extended, and this 
compression and extension is not confined to the outer 
layers of fibres, but affects those in the interior of the girder 
to a gradually decreasing extent, as their distance from the 
top and bottom of the girder increases, until, when a certain 



1 66 On the Strength of Structures. 

point is reached, the fibres are neither compressed nor 
extended, and hence retain their original length. 

This plane or surface of unaltered length, at or near the 
centre of the depth of the beam (when the material is nearly 
equal in tensile and compressive strength) is called the 
'neutral surface,' and the line in which this surface cuts 
any transverse section of the girder is called the 'neutral 
axis of the section.' 

The neutral axis of any section of a girder is, therefore, 
the line of demarcation between the forces of tension and 
compression exerted by the fibres crossing that section. In 
addition to these strains of tension and compression, there 
is a shearing strain, caused by the tendency of the weight 
to separate the part of the beam upon which it immediately 
rests from the adjoining part ; this tendency is resisted by 
the material, and the weight is thus transmitted to the ad- 
joining part, and by it to the next adjoining part, and so 
on -to the supports. In parallel flanged girders, this strain is 
chiefly resisted by the web. 

That there is no tensile strain upon the upper half of 
.such a girder may be shown by an experiment. If we 
take a girder of the class here referred to, either of wood or 
metal, and cut it across its upper surface, and then insert 
a thin piece of wood or metal into the saw-cut, simply to 
prevent the opening from closing again when the weight is 
put on, the beam will be found to be as strong as before ; 
but, on the other hand, the slightest notch on the under 
surface will weaken it considerably, and this will become 
apparent if the beam is tested. 

It has been previously stated, that the strain upon the 
fibres of the beam gradually decreases from the top and 
bottom to the neutral surface of the beam, and hence the 
nearer the fibres are to that point the less they contribute 
towards supporting the load, and the farther they are re- 
moved from it, the greater is the power which they have to 
assist in its support ; therefore, the neutral line is the part 



Beams and Girders. 167 

where holes, for fixing other parts connected with the girder, 
may be made with impunity. 

In correctly proportioned flanged girders, the position of 
the neutral surface is considered to pass through the centres 
of gravity of the transverse cross sections, and the inten- 
sity of stress on each flange is directly proportional to the 
distance of the flange from the neutral axis. The section 
of each flange should be so proportioned, that the intensity 
of the stress exactly corresponds with the resistance of the 
material to tension or compression. It must, however, 
be borne in mind that the material of the compression 
flange is subject to distortion, and the real resisting power 
of this flange is its power to resist distortion or crippling, 
and not absolute compression. 

The position of the neutral surface of a rectangular beam 
depends entirely upon the nature of the material ; if its 
tenacity and power of resisting compression are equal, then 
the neutral surface will be in the middle of the depth, but 
not otherwise. Cast iron, for example, has about six times 
the power of resisting compression that it has of resisting 
extension ; therefore the depth of material above the neutral 
surface will be to that beneath it as Vi is to V6, or as 1 is 
to 2 *449, or, in round numbers, as 2 is to 5 ; and it would 
only bear the saw-cut f of its depth, without loss of 
strength. 

Let fig. 20 represent an exaggerated view of a cantilever 
loaded at its outer end, and a b c d a portion of the beam 
before deflection ; let the upper edge, after deflection, be 
extended from the length b a to the length b <?, and the lower 
edge compressed from d clo> d f, then the lines across the 
two triangles represent the alteration of length of the inter- 
mediate fibres, the neutral surface g h dividing the depth of 
the beam into two equal parts. 

The total stress upon the fibres composing each half of 
the beam is the product of the area of half the beam multi- 
plied by the mean strain moon the fibres, and if the strain 



1 68 



On the Strength of Structures. 



upon the extreme fibres is 4 tons, the mean strain upon all 
the fibres will be one-half 4 tons = 2 tons, and the total 
strain upon either half of the beam will equal 2 tons multi- 
plied by the breadth of the beam, and by half its depth. 

Fig. 20. 




Further, as the lines across the triangles are proportional 
to the strains upon the several fibres, the centre of the ten- 
sions and compressions (that is to say, their resultants) will 
coincide with the centre of gravity of the two shaded tri- 
angles, which will be -| of their height from the neutral axis, 
and hence the distance between the two centres of strain 
will be § of the depth of the girder ; and, supposing one of 
them to act as a fulcrum, then the moments of the forces 
acting about that point will be, on one side, the product of 
the weight multiplied by its distance from the section of the 
girder in question, and, on the other side, the product of the 
tensile or compressive strain multiplied by § of the depth of 
the beam. 

If we knew in all cases the position of the neutral axis 



Beams and Girders. 169 

and the tensile strength of the material, we could then com- 
pute the strength of rectangular beams without any addi- 
tional data ; but without such precise knowledge, the best, or 
at least the easiest, method of determining the resistance of 
rectangular beams is to make a series of comparative ex- 
periments upon model beams, and determine their strength 
and deflection. From these experimental results a constant 
number may be deduced for each description of material. 
Such experiments have been made, and the table at page 
176 contains the constant numbers for some of the materials 
which are most commonly used in works of construction. 

The strength of flanged girders, of similar section, varies 
inversely as their lengths, and directly as their depths, and 
as the sectional area of their flanges ; for if we double the 
length of either of the beams in the foregoing examples, 
then only one-half the weight upon the long arm of the lever 
would be required to break the beam ; or if, on the other 
hand, we double the depth, we thereby double the strength, 
because the short arm is twice the length, and hence the 
flange, from its position, would be able to resist twice the 
weight acting at the end of the long arm of the lever ; or if 
we double or increase the area of either flange, we also 
double or increase the strength in the same proportion. 

It may be stated, as a general rule, that the strength of 
solid rectangular beams varies inversely as the length, 
directly as the breadth, and directly as the square of the 
depth, but up to a certain extent only — namely, so long as 
the said beam can be kept from twisting. For if we double 
the length of the beam, the resisting power of the section at 
any particular part will still remain the same, so that the 
actual weight required to overcome it will thus be reduced to 
one-half, because it acts now with twice the leverage; or, on 
the other hand, if we double the breadth of the beam, we 
thereby double the number of the resisting fibres, but do not 
alter the leverage, and consequently it has twice the strength ; 
but if we double the depth, we then have twice the number 



170 



On the Strength of Structures, 



of fibres and also twice the leverage, and therefore we have 
four times the resisting power. Hence, the strength is as the 
square of the depth. 

The strength of square beams varies inversely as the 
length, and directly as the cube of the side of the square, 
because ; if we double the side of a square beam, we then 
have four times the number of fibres or molecules, acting at 
twice the leverage, which gives a resistance equal to eight 
times that of the original beam ; in other words, the strength 
is as the cube of their sides. 

The strength of cylindrical beams varies inversely as their 
length, and directly as the cube of their diameter, for the 
same reason as that stated for the square beam. 

The strongest solid rectangular beam, which can be cut 
out of a round log of timber, has a cross section, the square 
of the breadth of which is equal to one-third of the square of 
its diagonal. In other words, the proportion of breadth to 
depth is as 5 to 7 nearly. Hence, we have the following 
construction for cutting the strongest beam out of a round 
log. 

Fig. 21. 




Describe a circle equal to the size of the log, and draw a 
diameter a d' 3 divide it into three equal parts ab,b c, and 



Beams and Girders. 171 

c d; erect perpendiculars at b and c upon opposite sides 
of the diameter intersecting the circle, and then join the 
points in which the diameter and perpendiculars intersect 
the circle, and the rectangle so formed is the section of the 
strongest beam that can be cut from the log. 

Rectangular beams are often made much deeper, in 
proportion to the breadth, than the beam given above, 
but they have to be kept from twisting by resorting to cross 
bracing or otherwise; still, for independent beams, the above 
proportion should always be employed where practicable. 
In some instances, the strength of the web of a cast-iron 
girder, considered as an independent rectangular beam, is 
added to the strength of the flanges, and a much greater 
apparent strength is thereby assumed than is justified either 
by experiment or in the practical constructions of the work- 
shop. 

The strength of a square tube when used as a girder, with 
its sides placed in a vertical position, is to the strength of a 
round tube of equal thickness and span, and having a dia- 
meter equal to the side of the square tube, as 17 is to 10. 
The strength of a similar round tube, having a diameter 
equal to the diagonal of the square tube, is to that of the 
square tube as 100 is to 85. 

With square and round tubes of equal thickness and weight, 
their peripheries will be equal, and, when the sides of the 
square tube are vertical, their relative strengths are as 105 is 
to 100. The square tube, when placed with its sides in a verti- 
cal position, has thus a slight advantage over the round tube ; 
but in such instances as crane-posts, which are subjected to 
transverse strains in all directions, by the load being slewed 
upon them all round the circle, the round form is preferable? 
because it is much stronger than a square tube of equal 
weight, when the load acts upon it in the direction of its 
diagonals, there being then so much more of the material 
in the vicinity of the neutral axis. 



172 On the Strength of Structures. 

Beams of Uniform Strength. 

For most arrangements of the load on. a beam, the bend- 
ing moment at various points of the length varies. It is not 
generally necessary, therefore, that the section of the beam 
should be uniform from end to end, and material may be 
economised by reducing the section where the bending 
action is less. When a beam is so proportioned that the 
moment of resistance of the section, at each point of its 
length, is proportional to the bending moment at that point, 
the beam is called a beam of uniform strength. 

It will only be necessary to consider two kinds of load- 
ing — that in which the load is concentrated at one point 
of the beam, and that in which the load is uniformly dis- 
tributed over the beam. In the former case, the bending 
moment is. greatest at the place where the load is applied, 
and in the latter case, the bending moment is greatest at 
the centre of the beam. In both cases there is no bending 
moment over the supports. There are also two ways in 
which the section of the beam may be varied so as to fulfil 
the conditions of uniform strength. The breadth of the beam 
may be maintained constant, and the depth varied, or the 
depth may be maintained constant, and the breadth varied. 
If the beam is a flanged beam, the thickness of the flanges 
is supposed to be constant throughout the beam in either 
case. For a beam of uniform strength and uniform depth, 
carrying a single fixed load, the plan of the flanges should 
be two triangles, with their bases united in a line, passing 
through the point at which the weight is applied and their 
apices at the supports. But if the flanges are of uniform 
breadth, then the side-view of the girder should be a triangle, 
the base of which is the top flange, and the apex of which is 
directly under the load. For a beam of uniform strength and 
uniform depth, carrying a uniformly distributed load, the 
plan of the flanges should be formed by the overlap of two 
parabolas, whose vertices are at the ends of a line drawn 



Beams and Girders. 173 

across the centre of the girder, equal in length to the breadth 
of the flange. But, if the breadth of the flanges is uniform, 
then the depth must be variable, and one flange may be 
straight and the other curved in the side-view. The curved 
flange of the girder should be a parabola whose axis is ver- 
tical, and its vertex at the centre of the girder. This form 
should also be adopted for a girder which is to carry a single 
moving load, such as the gantry to carry the crab of a 
travelling crane, and for the girders of bridges to carry 
weights upon a single line of rails. 

Flanged cantilevers (if intended to be of uniform strength) 
should be of exactly the same form as the half of one of the 
above girders, according to the manner in which they are 
loaded. There are often, however, practical difficulties in 
the way of making beams of the above forms, and they are 
frequently made half as deep at the ends as in the middle, so 
as to obtain an abutment for fixing, and they are curved so 
as to include a parabola drawn through the three points thus 
determined. 

In order that the student may readily ascertain the 
strength and deflection of any rectangular or cylindrical beam, 
it is necessary, as already stated, owing to the defective state 
of our knowledge of this part of the subject, to use certain 
numbers called constants, which have been determined at 
various times by different persons. 

Practically speaking, there is a great objection to the use 
of such numbers, but until the position of the neutral axis of 
such beams as are employed in practice is accurately deter- 
mined, it is the only course open ; and if an engineer has to 
make a structure of some new sort of timber or other ma- 
terial, upon which no previous experiments have been made, 
he will have to make experiments upon model beams of the 
material, to determine the constant number, before he can 
proceed with any proper feeling of certainty that, in his 
structure, he has obtained the requisite strength with the 
minimum quantity of material. 



174 On the Strength of Structures. 

The following table contains, in the column marked 
'Value of Strength/ the constants required for ascertain- 
ing the ultimate strength of a rectangular beam, of a given 
size, of most of the materials commonly used in structures ; 
and the strength or breaking weight in lbs. of any such beam, 
when supported at each end and loaded at the middle, may 
be found by multiplying the breadth in inches by the depth 
in inches squared, and by the constant number in the column 
' Strength, ' and dividing the product by the length of the 
beam in feet. 

The value of the constants for strength may be found, by 
taking a bar one inch square, twelve inches between the 
supports, and observing how many pounds' weight applied 
in the middle is required to break it ; the number of pounds 
so ascertained is the constant. But the experimental beams 
need not be of the above dimensions ; any convenient size 
of beam may be used for the experiment, the larger the 
better, and the breaking weight of the experimental beam is 
then reduced to the weight required to break a beam of the 
above dimensions. 

For example, the constant for the strength of teak, con- 
tained in the table, was determined from three experiments 
made by Barlow upon beams of that material, seven feet 
long by two inches square, which broke with a mean weight 
of 938 lbs. 

It has been already stated, that the breaking weight of a 
rectangular beam varies as the breadth and the square of 
the depth, and inversely as the length, or thus : 

breadth In inches x depth squared in 
Breaking weight in lbs. = inches x constant 



length in feet ; 

and all these particulars are furnished by the experiment, 
except the constant, which may be ascertained by the inver- 
sion of the above statement ; thus : 

~ length in feet x weight in lbs. 

Constant = , . , . & . — = , f . — , — 

breadth in inches x depth m inches squared. 



Beams and Girders. 175 

Then, by filling in the known quantities and working out the 
sum, we obtain the constant; thus : 

Constant = — — ~ = 820, which is the number placed opposite teak 
in the table. 

To find the breaking weight of a beam of any of the mate- 
rials in table : 

Breadth in inches x depth 

in inches squared x constant , . . . . 

--3^ — = breaking weight m lbs. 

length in feet s s 

For example, find the breaking weight at the centre of a 
beam of Memel deal, 14 inches deep, 10 inches wide, and 
20 feet between the supports : 

ioxi4xi4x545 = 534IolbSj 
20 

To find the breadth of beam required, so that it will just 
break with a given weight, when the depth and length be- 
tween supports are given : 

Length in feet x breaking weight in lbs. , ,.,, . , . . , 

. , . — : — , f 2 = breadth required in inches. 

depth in inches squared x constant 

To find the depth of beam required to support a given 
weight, when the breadth and length between supports are 
given : 

Length in feet * breaking weight in lbs. = d ± ^ inches ± 

breadth m inches x constant 

And the square root of the result will be the depth required 
in inches. 

For example, find the depth of a beam of English oak 
required to support 2\ tons at the centre with safety, to be 
10 inches broad and 25 feet between the supports. In this 
case we must first determine how many times the breaking 
weight of the beam is to exceed the working load ; in perma- 
nent structures it should be ten times, but in temporary 
constructions it may be reduced to six times. In this ex- 



176 



'On the Strength of Structures. 



ample we will take the former, and then the breaking strength 
becomes — 

2| x 10=25 tons, and 2 5 * 2 5 * 2240 = 

10x557 J °' 

and the square root of 251-3=15-8, the depth, in inches, of 
beam required to meet the above condition. 



Constants of Strength and Deflection. 
The latter will be explained hereafter. 

TABLE XXXIX. 



Nature of Material. 


Value of 
Strength. 


Value of 
Deflection. 


Authorities. 


Teak 


820 


5588 


\ 


English Oak 








557 


3359 




Canadian Oak 








588 


4964 




Dantzic Pak 








485 


2757 




Adriatic Oak 








461 


2255 




Ash . 








675 


3807 




Beech 
Elm . 








518 

337 


3133 
1620 


\ P. Barlow. 


Pitch Pine . 








544 


2837 




Red Pine . 








"447 


4259 




New England Fi 


r 






3 6 7 


5072 




Riga Fir . 








369 


3079 




Mar Forest Fir 








381 


2013 




Larch 








284 


2437 




Norway Spar 








491 


3374 




Mahogany, Spanish 






425 


2906 


\ 


,, Honduras 






637 


3571 


\ Tredgold. 


Memel Deal 






545 


4500 


Christiana Deal . 






686 


4176 


j 


Cast Iron . . 
Do. 






2548 
2532 . 


1 41 740 


Banks. 


Wrought Iron, Swedish 




3473 


64221 


> Kircaldy. 


Hammered Steel 


6403 


78822 



The relative strength of beams of rectangular or other 
sections, supported and loaded in any other manner, will be 



Beams and Girders. 177 

to that found by the foregoing rules, in the various propor- 
tions given at page 160. 

With the flanged girder, the case is widely different, for 
in its construction we have the means of placing the ma- 
terial (whether of wrought or cast iron) in the most advan- 
tageous position, to resist the strain, and, hence, it would be 
a deliberate waste of material, to make a beam of either of 
those substances of the form employed for a timber beam. 
Having this power, we place the bulk of the material at the 
greatest distance from the neutral axis. 

In designing flanged beams, the nature and amount of the 
strain on each part of the flanges should first be ascertained, 
and then, if the proper amount of material to resist the 
strain is introduced at each point, the greatest economy of 
material will be attained. 

It has been previously explained that the top flange will 
be compressed, and the bottom flange extended, or, in other 
words, that the material in the top flange will be subjected 
to a compressive, and that in the bottom flange to a tensile 
stress. The amount of these strains can be found by consider- 
ing each half of the beam a b c, in fig. 22, as a bent lever, the 
long arm being equal to the distance between the weight and 
the support — namely, in this case, ten feet — and the short arm 
to the depth of the beam, or in this case two feet The force 
acting at the end of the long arm will be the upward resist- 
ance of the support, in this case equal to half the weight, or 
six tons ; and by the principle of the lever, if we multiply the 
weight acting at the end of the long arm by its length, and 
divide the product by the length of the short arm, we obtain 
the weight that will be required at the end of the short arm 
of the lever to balance the upward resistance of the sup- 
port. Thus, in the case shown, 10 multiplied by 6, and the 
product divided by 2 = 30 tons, the total strain on one 
flange. 

The total amount of strain on the top flange is the same 
as that on the bottom flange, as indicated in fig. 23. 

N 



i 7 8 



Oft the Strength of Structures. 




But the strain on the top flange is compressive, and that on 
the bottom flange is tensile. Supposing that the greatest safe 



Beams and Girders. 179 

intensity of stress in tension, for the material of the beam, 
to be ii ton per square inch, the bottom flange must have 
30-7-11=20 square inches of sectional area. It may be 
10 inches wide and 2 inches thick, for instance, or of any 
other dimensions giving the same area. 

Professor Hodgkinson found, by a number of experiments, 
that the top flange of a cast-iron girder only required to be 
£th of the area of the bottom, or, in other words, that cast iron 
might be subjected to a compressive stress of nine tons per 
square inch, but yet we find in practice that the top flange is 
seldom made less than Jth of the area of the bottom flange. 
The reason is that, if the top flange is made onlyith of the 
area of the bottom flange, and of sufficient width to give 
the required lateral stiffness to the upper part of the beam, 
it must be very much thinner than any other part of the 
girder, which would induce an initial strain upon some part 
of the girder by unequal contraction, due to the different rate 
of cooling after being cast 

Take, for example, the top flange of the girder in question. 
If it were made £th of the area of the bottom flange, it would 
only contain 20-^6=3! square inches ; and if it were made 
4 inches wide, then it would only be 3^- •— 4 = f ths of an 
inch thick, whereas the bottom flange would be 2 inches and 
the web i\ inch thick ; but by making the top flange Jth 
of the area of the bottom its section would be 20 -*- 4 = 5 
square inches, and if made 4 inches wide it would be 5 -5-4= 1 J 
inch thick; that is, equal to the thickness of the web, a 
much better proportion. Some experience is necessary, to 
determine the best form and dimensions, so as to meet not 
only the theoretical requirements of strength, but the con- 
ditions imposed by practical experience in the foundry. 

By assuming a compressive stress of 6 tons per square 
inch of section, an area of 30 ~- 6 = 5 square inches will 
be required to produce the same result, and the flange may 
be made 4 inches wide and i± inch thick, .or 5 inches wide 
and 1 inch thick • but the former would be preferable, because 



1 80 O11 the Strength of Structures. 

the cooling in the mould would be more uniform, and there- 
fore the contraction of the top flange would be more nearly- 
equal to that of the other parts of the girder. 

If the girder is to be of wrought iron, a similar method is 
adopted, but, with that material, the strain per square inch 
which is generally allowed is 4 tons for compression and 5 
tons for tension, and, according to the Board of Trade regu- 
lations, it is 5 tons per square inch both for tension and com- 
pression, which simplifies the calculation, is easily remem- 
bered, and is sufficiently near for ordinary purposes. At the 
same time, it would not be applicable to structures exposed 
to contingencies, such as the surging of slings by falling- 
weights. 

Deflection of Beams. 

When a beam is supported at each end, the distance to 
which the middle of the beam is forced down below its 
original position, by the load, is termed its deflection, and in 
parallel girders, with the flanges of uniform strength, the 
deflection curve is found to be circular. 

The deflection of solid rectangular beams varies directly 
as the load and the cube of the length, and inversely as the 
breadth and the cube of the depth. 

In flanged girders, the amount of deflection varies directly 
as the load, the sum of the areas of both flanges, and the 
cube of the length, and inversely as the product of the areas 
of the two flanges multiplied together and the square of the 
depth of the web. 

It appears from the reasoning and experiments of Pro- 
fessor Barlow, that the deflection of a rectangular beam, fixed 
at one end and loaded at the other, is equal to that of a 
beam of twice the length, supported at both ends and loaded 
at the centre with double the weight. The deflection varies 
as the cube of the length, and if we reduce the girder until it 
is equal in length to the semi-girder, the ratio of the deflections 
will then be as the cubes of the lengths; namely, as 1 is to 8. 



Beams and Girders. 181 

In other words, the deflection of a semi-girder will be eight 
times that of a girder, equal to it in all respects, when the 
latter carries double the load. If we now reduce the weight 
upon this shortened girder— say \ — so as to make it equal to 
that carried by the semi-girder, then we reduce its deflection \, 
and hence the amount of deflection of the semi-girder will be 
sixteen times that of the girder when they are equally loaded. 
It has already been shown that the strength of the girder is 
four times that of the semi-girder, whereas from the above 
reasoning the stiffness of the girder is shown to be sixteen 
times as great as that of the semi-girder. 

If we require two beams of the same breadth, but of 
different lengths, to be equal in stiffness, then their respective 
depths must be in proportion to their lengths, because de- 
flection, or want of stiffness, varies directly as the cube of the 
length, and inversely as the cube of the depth, or as the 
cubes of both these dimensions. 

For example, let these lengths be 24 and 12 feet; then if 
the latter is 12 inches deep, the former will have to be 24 
inches deep to be equally rigid, whereas it would be equally 
strong if made 1 7 inches deep. 

If the beams are equal in depth, but of different lengths, 
and are required to be equal in stiffness, then their breadths 
must be as the cubes of the lengths. Taking the same 
lengths as before — 24 and 12 feet — the breadths would have 
to be in the ratio of 24-cubed to 12-cubed; that is, as 13824 
is to 1728, or as 8 is to 1. In other words, the long beam 
would have to be eight times as broad as the shorter one to 
be equally rigid, whereas it only requires to be twice as broad 
to be equally strong. 

We have already seen that the strength of a rectangular 
beam varies as the square of the depth, multiplied by the 
breadth, and divided by the length, but the stiffness varies as 
the cube of the depth multiplied by the breadth and divided 
by the cube of the length. 

The stiffness of cylindrical beams varies as the fourth 



1 82 On the Strength of Structures. 

power of the diameter, and inversely as the cube of the 
length. 

The deflection of similar girders also varies with the 
manner of loading, and if the load is uniformly distributed 
over a beam supported at both ends, the deflection will only 
be fths of that of the same beam, loaded with the same weight 
collected at the centre of its length ; and the deflection of a 
semi-girder uniformly loaded is only fths of the deflection 
caused by the same weight acting at the end. 

The foregoing investigations and results of experiments 
upon the deflection of beams are true, provided the visible 
limit of elasticity of the material is not exceeded, but they 
are not true of the ultimate deflection, because the law of 
deflection is very uncertain after the elasticity of the mate- 
rial has ceased to be sensibly perfect, and this condition is 
reached long before rupture takes place. 

The constant numbers which are used for ascertaining the 
deflection of rectangular beams are contained in Table 
XXXIX. page 176, in the column marked 'Value of Deflec- 
tion,' and these constant numbers are deduced from the 
experiments in the following manner : 

The deflection, in inches, of rectangular beams supported 
at both ends and loaded at the centre is equal to — 

the cube of the length in feet x weight on beam 

Deflection i _ in lbs. 

in inches J breadth in inches x the cube of the depth in inches 
x constant. 

And all these elements are determined by the size of the 
beam, the weight applied, and the deflection which took 
place during the experiment, excepting the constant, which 
is found by the inversion of the above statement ; thus — 

the cube of the length in feet x weight on beam 

~~ breadth in inches x the cube of depth in inches x 
deflection in inches. 

Take for example the constant for deflection of teak, 



Beams and Girders. 183 

which has been determined from the same experiments as 
those from which the constant for strength was obtained, 
but with this difference, that the weight upon the beam is 
not the breaking weight, but the greatest weight the beam 
bore, while its elasticity remained visibly perfect, and the 
deflection is that which was caused by that weight. These 
two quantities are stated by Barlow to have been 300 lbs., 
and 1*151 inch ; then, filling in the quantities, we have — 

Constant = - ? * 3g°_ = _343 * 3°^_ = 
2 x 2 3 x 1*151 2 x 8 x 1*151 

which is the number opposite teak, in the column headed 
'Value of Deflection,' and all the constants D in Table 
XXXIX. page 176, are calculated in this way, from experi- 
ments carried out by different individuals. 

The deflection of timber beams should not exceed in 
practice ^^th of their length, and it appears, from Tredgold's 
experiments on cast iron 5 that if the deflection of bars of that 
material exceeds xJo-th of their length, a permanent set is 
caused; from Kircaldy's experiments on bars of wrought 
iron and steel, that a deflection exceeding -^-th of the length 
causes a permanent set, upon bars of those materials. 

To find the size of beam, supported at both ends and 
loaded at the centre, capable of supporting a given weight 
with a given amount of deflection : 

The cube of the length in feet x 

weight in lbs. f breadth in inches x cube of 

deflection x constant ~ I depth in inches. 

For example, find the size of a beam, of English oak, sup- 
ported at each end and loaded at the centre with a weight 
of 2\ tons, the distance between the supports being 25 feet, 
and the deflection not to exceed ¥ J^th of the length • the 
deflection in inches will be — 

2K x 12 x — o- = - 6 - = o = *° 2 5 of an mch: 
•> 480 480 8 J ' 

then 25 s x 2-5 x 2240 _ . I77 = f the breadth x the cube 
•625 x 3359 ** / /«■ \ of the depth : 



1 84 On the Strength of Structures. 

and, assuming 10 inches for the breadth, we have 4_ZZ4 = 4177-4 = 

the cube of the depth, and the cube root of 4177*4 = 16 1 = the 
depth of the beam required. 

If the beam is to be square, the fourth root of the quotient 
will be the side of the square ; thus — 

The fourth root of 41774 = 14 '3 nearly, for the side of the square. 

If the beam is to be cylindrical, first multiply the quotient 
by 17, and then extract the fourth root, which will be the 
diameter of the beam required, because the deflection of a 
cylindrical beam is 17-ths that of a square beam, all other 
circumstances being the same, and hence it requires 17-ths 
the material to render it equally rigid. The diameter 
of a circular beam will therefore be the fourth root of 

41774 x 17 = 16-3 inches = the diameter of the beam. 

If the beam is to be rectangular, either the breadth or 
depth must be fixed, and the other dimension will be found 
thus. 

To find the depth of beam required to carry a given 
weight, with a given amount of deflection, when the length 
and breadth of the beam are given : 

The cube of the length in feet x weight 

in lbs^ — — _ = the cube of the d h 

breadth in inches x deflection x con- 
stant 

then the cube root of the result is equal to the depth in 
inches required. 

To find the breadth of beam required when the weight to 
be carried, the amount of deflection, and the length and 
depth are given : 

The cube of the length in feet x weight 

in lbs. _ f the breadth in inches 

theTube of the depth in inches x ~ I required. 

deflection x constant. 



Beams and Girders. 185 

To find the weight which will cause a given amount of 
deflection upon a beam : 

Breadth in inches x the cube of the depth in inches 

x deflection x constant. . . . ,. 

-r r — Fit — ; 7—- = weight in lbs. 

the cube. of the length in teet & 

To find the deflection of a beam supported at both ends 
with a load uniformly distributed over its entire length, take 
fths of the result, given by the rule to find the deflection of a 
beam loaded at the centre. 

To find the deflection of a semi-beam, supported at one 
end and loaded at the other, multiply by 16 the deflection 
of the same beam supported at both ends and loaded at the 
centre. 

And, lastly, to find the deflection of a semi-beam, sup- 
ported at one end, with the load uniformly distributed over 
its entire length, multiply by 6 the deflection of the same 
beam supported at both ends and loaded at the centre. 

The relative deflection of similar beams, each supporting 
the same weight, with the supports and load in various 
positions is, as follows : 

Position of Support and Load. 

Relative 
deflection. 
When supported at both ends and the loads evenly \ 

distributed, the deflection is . . • J 

When supported at both . ends and loaded at the 1 o 

centre, the deflection is . . . . . S 

When supported at one end and load distributed, 

the deflection is ..... . 

And when supported at one end and loaded at the "I « 

other, the deflection is . . . .J 

The above table teaches a very instructive lesson to en- 
gineers, and shows how wrong in principle it is, to have 
wheels, pinions, or pulleys, which have hard work to perform, 
overhanging the bearing upon which they are supported, and 
in the case of machines, where such an arrangement is 



1 86 On the StrcngtJi of Structures. 

rendered necessary, the shaft should then be made of pro- 
portionately increased diameter in the bearing, and tapered 
off, being not abruptly, but gradually diminished to the 
diameter of the remaining portion of the shaft. 

These relative deflections of the beam and semi-beam, 
loaded in different ways, apply equally to beams of any sec- 
tion, so that if the deflection of the simple girder, supported 
at each end and loaded at the centre, be found, that of the 
others can be ascertained by simple multiplication, as above 
stated, 

If the student requires to find the deflection of a beam of 
any other form of section than the rectangular or circular, 
he must first deduce the constant for that particular form of 
section, from an experiment upon a similar beam, and then 
proceed in a similar manner, or else he may make an ex- 
periment on his own account, which will be useful to himself 
in other respects. 

Resilience of Beams. 

The resistance of beams to transverse impact, or, in other 
words, to a suddenly applied load, is termed their ' resilience,' 
and it follows a very different law from that of their strength, 
for it is simply proportional to the mass or weight of the 
beam, irrespective of the length, or the proportion between 
the depth and breadth. 

It appears from the published experiments and statements 
of the Railway Commissioners, that a beam 1 2 feet long will 
only support \ of the steady load that a beam 6 feet long 
of the same breadth and depth will support, but that it will 
bear double the weight, suddenly applied, as in the case of 
a weight falling upon it ; or if the same weights are used, the 
longer beam will not break by the weight falling upon it, 
unless it falls through twice the distance required to fracture 
the shorter beam. 

This law was apparently proved by a large number of 



On the Strength of Gearing. 187 

experiments carried out for the Railway Commissioners, in 
which the beams appear to resist the sudden application of 
the load, by gradually absorbing the work accumulated in 
the falling weight, and to bend through a certain distance, 
until the work done in bending the beam through that 
distance is equal to the work accumulated in the weight, due 
to the distance which it has fallen. Hence a very strong 
beam may be broken, if it is not sufficiently elastic to bend 
through the required distance, and thus absorb the vis 
viva of the falling weight. 



CHAPTER XIII. 

ON THE STRENGTH OF GEARING. 

In the chapter on torsion, reference is made to the strength 
of spindles and shafts, employed in conveying power from 
one point to another, to give motion to machinery. It is 
equally important for the engineer to know, how to propor- 
tion the other parts of the transmissive machinery — the spur- 
wheels and bevil-wheels, for instance — which are the agents 
by which power is transferred from one shaft or spindle to 
another. More especially is it important, to be able to cal- 
culate the strength of the teeth of wheels, these being the 
agents through which the driving forces are directly trans- 
mitted. 

When properly made, the teeth of the two wheels act 
against each other, as the wheels revolve, with comparatively 
little thrust, noise, or friction. To secure proper mutual 
action of the teeth, their form must be determined on the 
principles which are explained in Professor Goodeve's 
' Treatise on Mechanism.' But, besides determining the 
best form for the teeth, the engineer requires, also, to ascer- 
tain their size for any given case, and this is usually simply 
a question of strength. 



1 88 On the Strength of Structures. 

In estimating the strength of the teeth of mill-gearing, 
we have to attend, first, to the strength of the material of 
which the gearing is made ; second, to the forces which act 
on the teeth, due to the power transmitted ; and, third, to 
the way in which the teeth resist fracture under the action 
of the ascertained forces. We shall best explain the method 
of proceeding, by taking an example. Suppose it is required 
to determine the dimensions of the teeth of a wheel on the 
main axle of a thirty-ton crane. Let the barrel be four feet 
diameter, and the wheel six feet diameter, measured to the 
pitch-line. Further, let it be assumed that the tension on the 
chain which is coiled on the barrel is reduced from 30 tons to 
7^ tons, as the result of the mechanical advantage of the 
chain tackle. The total load on the teeth of the wheel will 
be 7^ tons, multiplied by the radius of the barrel, and divided 
by the radius of the wheel ; that is, 7^ x 2-5-3=5 tons, 
or 11,200 lbs. We may presume, that this load is distributed 
over two teeth, there being always at least two teeth in full 
bearing at the same time. The load on one tooth is there- 
fore 1 1, 200 -r- 2 = 5,600 lbs., which acts on the tooth like 
a load on the end of a projecting cantilever, tending to break 
it by transverse fracture at the root. 

Let it be next assumed that the wheel is of cast iron, and 
that, for safety, the strain on the tooth is not to exceed ^th 
of that which would fracture it. A cast-iron bar of good 
quality, 1 inch long and 1 inch square, loaded at the end^ 
would break with about 6,000 lbs. The wheel tooth is to be 
considered, as in similar conditions to such a bar, or, in other 
words, it is in the condition of a beam loaded at one end 
and fixed at the other, and its resistance to fracture is pro- 
portional to the square of its depth (that is, the thickness of 
the tooth) to the breadth (that is, the width of the face 
of the wheel) and inversely as the length (that is, the 
projection of the tooth measured from the root to the 
point). 

As the length and thickness of the teeth of wheels are 



On the Strength of Gearing. 1 89 

usually in some definite proportion to the pitch, it will now 
be necessary for the student to assume, to the best of his 
judgment, a suitable pitch of tooth for the required purpose, 
which will give the length and thickness. For example, 
assuming the pitch to be 2-5 inches, the length will be 1*875 
inch, and the thickness at the root 1-55 inch, the breadth 
across the wheel being three times the pitch, or 7-5 inches. 
Squaring the depth of the tooth, multiplying by the breadth 
and the strength of the iron, and then dividing the product 
by the length of the tooth, we get — 

I-55 2 * 7-5 x 6°°°. = 66o Ib 

1-875 
the ultimate strength of one tooth ; and the double of that, 
namely, 115,320 lbs. for the two teeth, that are supposed to 
be in gear. The ratio of this to the strain upon the teeth 

will therefore be-^^ 2 °, or 10-3, the ratio of the strength 
11200 ° 

to the working load. Should the assumed size be found 
either too strong or too weak, the assumed pitch must 
be decreased or increased until a suitable tooth is dis- 
covered 

In practice, the strength will much depend upon the 
accuracy of the adjustment of the gear, for if the teeth bear 
only at one end — a condition frequently seen — then the great 
advantage to be derived from a broad wheel is necessarily 
lost, and might as well not have been provided. In addi- 
tion to proper adjustment, a great increase of strength is 
gained by flanging the teeth of both wheel and pinion up to 
the pitch-lines ; this arrangement is now generally adopted 
for wheels of importance. 

In determining the substance to be given to the teeth of 
wheels to afford a given amount of strength, it has to be 
kept in view that such wheels, and the pinions especially, are 
subjected to rapid wear when in daily use, thus reducing the 
thickness of the teeth ; in other words, the depth of the 



190 On the Strength of Structures. 

beam and its strength, which is as the square of its depth. 
Hence it is necessary to make some allowance for the 
future wear in the strength of the original construction. 

From the circumstance that the pinion, in a given period, 
revolves so many times oftener than the wheel, the usual 
custom of making the teeth of both with the same allow- 
ance for wear may seem to be incorrect, and so far that is 
the case ; but still, as a rule, there are practical objections 
in the way of the more correct arrangement, which prevent 
its general application, although for special purposes it 
is sometimes otherwise. Thus, for gunpowder machinery, 
where great pains are taken, and where gun-metal and horn- 
beam work together, it is usual to reduce the metal and 
add a corresponding extra thickness to the wood. 

In the foregoing remarks, cast iron is chiefly referred to, 
because it is used more than any other metal for wheel 
purposes. But that material is not selected on account of its 
special fitness or superiority in any respect, so far as the 
duty to be performed is concerned ; it is chosen more on 
account of its cheapness, and because it may be readily cast 
into any form of wheel. Such considerations have great in- 
fluence in the settlement of such points, and particularly so 
in this case, for, owing to the peculiar form given to spur 
and bevil wheels, it is much easier to cast them than to 
forge them ; indeed, to make large toothed wheels by forg- 
ing is scarcely practicable, on account of the cost. For 
smaller wheels, termed pinions, and where a great number 
are required of a definite size, it is perfectly easy to make 
them by forging. Simple dies are prepared, in which a 
roughly shaped, viscous mass of white-hot wrought iron is 
placed, and then subjected to the blows of a steam-hammer. 
This, together with the aid derived from a taper punch, 
driven through the centre, forces the soft iron into every 
crevice of the die. By such means, wrought iron is used for 
wheels to some extent, and the dies may be so formed that 
the teeth will be flanged up to the pitch-lines, and pinions 



On the Strength of Gearing. 191 

so made are at least three times stronger than the same 
forms when made of cast iron. 

In circumstances where only one pinion or a few pinions, 
made of wrought iron, are required, it is more convenient (in 
order to avoid the cost of the dies) to forge them into solid 
blocks, and then cut out the teeth afterwards. This arrange- 
ment, however, scarcely admits of flanges, on account of the 
cost of manufacture, and the want of flanges may be said to 
reduce the strength by one-third ^consequently, such wheels 
have only double the strength of cast-iron pinions or wheels, 
made with flanges. 

Of late years, the material called malleable cast iron has 
been employed for many such purposes ; that is to say, the 
wheels are made of cast iron in the ordinary manner, and 
then subjected to a course of annealing, while embedded in 
some substance rich in oxygen, which combines with a por- 
tion of the carbon in the iron, and leaves the metal malle- 
able. This process is the reverse of steel-making by 
cementation. Wheels made by this method may have 
flanges, and have double the strength of cast iron, and are 
used extensively where great accuracy is not essential, but 
it is found difficult to maintain the truth of the pitch and 
form of the teeth, during the annealing process. During this 
process the casting is kept for a long time at a red heat, 
and this frequently causes it to twist or warp. 

All difficulty is, however, now removed by the use of cast 
steel, which may be cast into any form in an earthen mould, 
in the liquid state, in the same manner as cast iron, and, when 
properly made, such cast-steel wheels have four times the 
strength of cast-iron wheels, the only objection being the cost, 
cast steel in this form is nearly as expensive as bronze. 

The amount of mechanical power that may be transmitted 
by a pair of wheels, depends entirely upon the speed at 
which they are driven ; this opens up another and entirely 
different question, from that of the strength of the teeth of a 
wheel for a crane. In ordinary mill-gearing a wheel that 



1 92 On the Strength of Structures. 

might be capable of transmitting 10 horses' power at 60 
revolutions per minute, will be able to transmit 20 horses' 
power, if it is driven at 120 revolutions ; the same remarks 
apply to all the other parts, such as pulleys, and every kind 
of moving mechanism. But, practically, this is only true 
within certain limits, for, on reaching high velocities, other 
conditions of impact, vibration, and centrifugal force due to 
velocity step in, to keep the mechanical application within 
bounds, as depending on the material which is employed 
for the construction. 

Strength of Screws. 

A little consideration will show the student that the 
strength of the thread of a screw-bolt, or of its nut, or that 
of the tooth of a tangent wheel, depends on principles 
similar to those applicable to ordinary gearing. Looking at 
the longitudinal section of a portion of a screw, the thread 
will be found under the same conditions as a beam fixed at 
one end and with the load distributed uniformly, or pre- 
cisely similar to that of the tooth of a spur-wheel ; if, for 
example, the screw thread is made of a square form, it will 
have less breadth of root, and consequently less strength, 
than the same pitched screw, when made in the usual conical 
form, or even when made with the top and bottom rounded 
off, inasmuch as both of the latter shapes have a bioader 
base to be broken, or even detruded, thus affording a better 
resistance. 

Although the common angular thread, in one respect, may 
be considered as the strongest form, still it is found that, in 
another respect, it is not so strong as the square thread — 
namely, in resisting the influence of wear, as arising from 
the inclined plane action of the angle upon a corresponding 
angular surface in the nuts — which is remedied in the flat 
bearing of the square thread. Consequently the square thread 
is found, in practice, to be not nearly so likely to override 
the nut, by any excessive wear or by any inordinate straining. 



On the Strength of Gearing. 193 

Screw threads with a round top and round bottom are in- 
tended to combine both advantages — to possess the broad 
base of the angular thread, and at the same time to have 
some portion of the flat-bearing surface of the square thread. 
By this compromise they have, upon the whole, a decided 
advantage, which gives them the preference for many pur- 
poses. 

As a rule, screws act in one direction only ; such is the 
case "with screw-bolts and nuts ; but there are many ex- 
ceptions, such as the leading screw of a lathe or planing 
machine, or wherever the screw is employed as an agent to 
impart motion ; screws for the latter class of purposes are 
correctly formed when both sides of the thread are alike, 
because both sides have to perform the same duty. It is 
different, however, with the majority of screws, and espe- 
cially so in the example given — namely, the bolt and nut. 
There is no mechanical or manufacturing reason, why such 
screws should not be made at right angles to the axis, upon 
one side of the thread, so as to have the bearing surface 
similarly placed to that of a square thread, and with the 
other side inclined, as in the ordinary triangular thread. The 
threads would then be, in section, similar in form to the 
tooth of a ratchet-wheel, which acts only in one direction. 
Such a form has a self-evident advantage, in the case of the 
ratchet-wheel, but it would have a still greater advantage 
in the screw, because it would not only give the same 
breadth of base as the common angular thread, but that 
advantage would be combined with the complete flat bear- 
ing surface of the square thread, or, in other words, it is a 
form possessing the full advantage of both, and without 
any of their disadvantages. 

This form of screw thread was adopted by Sir William 
Armstrong, for the breech-screws of his celebrated guns, 
and its superiority in strength over the square threaded 
screw, formerly used, was so conspicuous as to leave no 
doubt in regard to its comparative advantage ; the form 

o 



194 On the Strength of Structures. 

is correct, in principle, for screws that act only in one 
direction, and, as the arts advance, must become general. 

Strength of Cutting Instruments. 

Similar principles might be advantageously applied in 
many other cases, but they are frequently lost sight of, and, 
although a great change for the better has taken place, of 
late years, more especially in regard to the forms given to 
cutting instruments of every description, so as to combine 
great strength with incisive penetration, we are yet far from 
having the minds of our workmen so imbued with the 
natural principles involved, as to keep them right, by an in- 
tuitive perception of what that right is, due to the natural 
reason which guides us in so many other things, and which 
is independent of men's inventions, and is the effect of time 
and training. 

To select a cutting instrument for the lathe or planing 
machine, as an example ; when such an article is formed on 
correct principles, with the side under the cutting edge 
nearly perpendicular to the work upon which it has to bear, 
in order to support the cutting edge, and to give great 
strength, and with the other side bevilled off from the cut- 
ting edge, like the saw-tooth, so as to give the knife-action 
of penetration ; such an instrument will be immensely more 
efficient, and many times more economical, than when the 
form given to the same instrument has been devised without 
knowledge and with reference to penetration only. Forms 
which are good in the estimation of the workman, have fre- 
quently neither strength nor penetration, the metal of the 
instrument being ground away where it should be left, and 
being left at the part where it should" be ground away. 

Such a lack of proper conditions arises, entirely, from not 
knowing the true principles, as there is no difference in cost 
or trouble. The result is a want of strength, which incapa- 
citates the instrument from grappling with the work, and 



On Columns. 195 

tiny shavings are peeled off by it, in a broken condition and 
in miserable quantity. An iron shaving of one continuous 
curl was shown in the 1862 Exhibition, 1140 feet in length, 
the length of the curl being 462 feet ; and some of the Royal 
Gun Factory iron shavings are \ of an inch in thickness by 
4J inches in breadth, and are curled up of any length, as if 
they were wooden spills. All this efficiency is due to the 
form which is given to the cutting instrument, which of 
course has to be supported by a machine of corresponding 
strength and power, but the perfection of cutting is entirely 
owing to the application of the true principles of strength and 
penetration, in shaping the small piece of cast steel which is 
used as an instrument. The mass of iron in the shaving in- 
dicates the strength of the tool, and the unbroken condition 
of the curl is an evidence of its fitness for the removal of 
the superfluous material, and at the same time shows that it 
is accomplished, without that useless expenditure of mechani- 
cal power, which is the case with more detrusive instruments. 
With badly formed tools, the shaving is broken up into small 
chips, to no useful purpose. Thus it is shown that * know- 
ledge is power.' . I^IL ^^^3- 



Ju4** 



]Uf^ 




CHAPTER XIV. 

X * 

ON THE STRENGTH OF LONG COLUMNS, 

■^ -^ 

The resistance of a long column, to loads acting in the 
direction of its axis, depends mainly on three -conditions : 
first, on the proportion which its length bears to its least 
transverse dimension ; second, on the form of the ends 
of the column ; and, third, on the direction in which the 
load acts, with reference to the axis of the column. 

In the case of short columns — that is, columns whose 
o 2 



196 On the Strength of Structures. 

length is only slightly in excess of their transverse dimen- 
sions — the material is ruptured by simple crushing alone; 
but when the height exceeds from three to eight times the 
least transverse dimension, according to the nature of the 
material, the rupture is caused partly by bending and partly 
by crushing ; and, when the length exceeds from twenty-five 
to thirty times the transverse dimension, then the column 
will fail by bending, and the material will be subjected to 
strains, similar to those of a beam, when under a transverse 
load; one side will be crushed and the other will be 
extended. 

There is, at the present time, no completely satisfactory 
theory of the ultimate resistance of long columns. Euler 
investigated, the law of resistance, on the assumption that the 
elasticity of the material remained perfect up to the point at 
which rupture was imminent. On this assumption, he found 
that the resistance of long cylindrical columns would be 
proportional to the fourth power of the diameter and in- 
versely as the square of the length. 

Hodgkinson found, however, by his experiments, that 
the ultimate resistance was proportional to a power of the 
diameter rather less than the fourth, and decreased in a 
much less ratio than the square of the length. 

Table XL. p. 197, gives the mean results of a number 
of experiments, made by Hodgkinson, and shows clearly 
that the strength of pillars depends greatly on the secure 
fixing of their ends. With both ends rounded, the strength 
is only \ of that afforded by similar pillars, having both 
ends flat, and abutting on flat surfaces. Pillars, with one 
end round and the other flat, have § of the strength 
of those with both ends flat. These facts show the ad- 
vantage derived from correct bearing surfaces in structures 
exposed to compression. The table also shows that pillars 
of timber, when the length exceeds seventeen times the 
diameter, are destroyed by bending, and that even those of 
seventeen diameters are partly bent as well as crushed. 



On Columns. 



197 







6 S % u 




,0 






vT 










a 


C v 1 S "^ . 




<u 


3 a fiij 


J2 


T3 T3 <U 


t/3 r-j 2 •-< vJ 

^ o.S S 


a 


S 3 c-5 "^ 


^3 S^G^ 

p "wo?: 

«6 ^^ s 




S 1 iiii 








3 § -all's 

q J3 £ > ci 




eight 
nder 
the 
ank. 


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Cs 'tf-OO 10 m - o> 


ON O W 00 O 


m unoo 00 00 Tf 


? 3 -fl ™ 


i-i 1-1 vo O co 


N 1>.00 cOvO vO CO 


Mean 

in lbs. 

whic 

pillars 


co vo" C\rn <l 


d! m" In N w N <t 








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M M M HH M 1-1 HI 


<*-. cJ 






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198 On the Strength of Structures. 

It was found in these experiments that a deflection was 
visible, in one case, with a little under ^ of the destroying 
load, and that, generally, there was a considerable deflection 
with between -J- and J of the destroying load. 

The visible result of the crushing strain upon short 
columns varies with the nature of the material, and rupture 
is caused either by splitting, shearing, or bulging ■ the 
former is characteristic of the hardest cast iron, the hardest 
description of stones, and also of timber. Crushing by 
shearing is exhibited by cast iron, when the height of the 
column is about one and a half time the transverse dimen- 
sion, whilst crushing by bulging takes place with short 
specimens of wrought iron, mild steel, gun-metal, lead, and 
other ductile metals. 

There are two other forms of crushing : first, crushing by 
wrinkling up, commonly called ' crippling ' or ' buckling ; ' 
and, second, by cross-breaking. The former is sometimes 
seen in columns of wrought iron, which are too long to be 
crushed by bulging, and too short to be bent by flexure ; 
and the latter occurs in cast-iron columns, when the length 
exceeds thirty times their diameter. 

The manner in which the column gives way depends 
upon the form of the ends of the column, in so far that, if 
the ends are rounded, the column is as liable to flexure as 
one of the same diameter and twice the length, with both 
ends flat and firmly fixed. Hence, if we break two similar 
columns, the one with the ends rounded, and the other 
with the ends flat, the length being about twenty times the 
diameter, the material in the one with rounded ends will 
be ruptured entirely by cross-breaking or transverse strain, 
while that of the other will be ruptured partly by crushing 
and partly by cross -breaking. 

The way in which the column yields also depends upon 
the direction of the load, which has heretofore been supposed 
to pass along the axis of the column. If the direction of 
the action of the load forms only a very small angle with the 



On Columns. 199 

axis of the column, it induces a strain upon the column 
at right angles to the direction of its axis, and it is then in 
a precisely similar condition to a beam supported at each 
end and loaded at the centre. 

In short columns, possessing sufficient rigidity to resist 
the bending strain caused by this indirect action of the 
load, the material is liable to be ruptured in detail, from the 
fact that the whole of it has not the opportunity of taking 
its full share of the work in resisting the load, and therefore 
cannot give due support to the smaller portion, upon which 
the load acts. 

There are a few practical deductions to be drawn from 
these three considerations : First, that a column should be 
made as short as possible, in proportion to diameter ; in 
other words, it should be capable of maintaining itself 
vertical by its stiffness. Second, that the ends of cast-iron 
pillars should be cast with broad bracketed flanges, con- 
siderably larger than the transverse dimensions of the 
columns at the centre, for although the flanges may not add 
to the strength, in a direct manner, yet they certainly add to 
the stability, and will prevent the column from bending ; 
that is, if the ends are made sufficiently stiff and strong to 
resist the thrust. Third, that the ends should be at right 
angles to the axis of the column, and placed so that the 
load may act upon the whole surface of the capital and 
base, and its resultant may pass directly along the axis of 
the column. 

As a matter of economy, all long columns should be of the 
form recommended for cylindrical beams — namely, that of a 
parabolic spindle — but this is a form which does not please 
the eye so well as the graceful outline of a taper column, 
and hence, no doubt, strict economy is often sacrificed to 
appearance. 

In considering the strength of columns, the probability 
of crushing by splitting or by shearing may be entirely 
neglected, because, practically, columns are never made so 



200 On the Strength of Structures. 

short that these forms of rupture are called into play, and, 
so far as timber and cast-iron columns are concerned, 
rupture will always take place by cross-breaking, and wrought- 
iron plate columns should either be properly stayed, to 
prevent buckling or bulging, or else sufficient material should 
be put into the section to resist the stress tending to cause 
local distortion or wrinkling up of the metal, until the cross- 
breaking or bending strain can come into play. 

The most reliable experiments upon the strength of 
columns are those of Hodgkinson, who carried out an 
elaborate series of experiments to determine the laws which 
govern the strength of cast-iron columns, and who also 
made a considerable number of experiments for the Railway 
Commissioners, in order to determine the best form of sec- 
tion of a wrought-iron tube, to resist compression, when 
the load is applied in the direction of its length. 

With respect to cast-iron columns, he found, first, that the 
strength of solid cylindrical columns with both ends rounded, 
and the length of which exceeded fifteen times the diameter, 
varied as the 376th power of the diameter ; second, that 
the strength of solid columns with both ends perfectly flat, 
when the length exceeded thirty times the diameter, varied 
as the 3* 6th power of the diameter nearly ; third, that when 
the diameters remained the same, the strength varied in- 
versely as the 17th power of the length; fourth, that the 
strength of hollow cast-iron columns, with rounded ends when 
the length exceeded fifteen times the diameter, varied as the 
difference of the 376th power of the external diameter and 
the 376th power of the internal diameter, divided by the 
17th power of the length ; fifth, that the strength of hollow 
cast-iron columns with both ends perfectly flat, when the 
length exceeded thirty times the diameter, varied as the 
difference of the 3*6th power of the external diameter and the 
3*6th power of the internal diameter, divided by the 17th 
power of the length ; sixth, that the strength of hollow cast- 
iron columns of the same diameter varied inversely as the 
17th power of the length, as in the case of solid columns. 



On Columns. 20 1 

From the same experiments he deduced the following 
rules, to assist us in ascertaining the strength of such 
columns : First, for solid cast-iron columns with both ends 
flat, when the length exceeds thirty times the diameter, the 
breaking weight, in tons, equals the product of the 3.76th 
power of the diameter, in inches, multiplied by 44*16 (a co- 
efficient deduced from the experiments), and divided by the 
17th power of the length, in feet. Second, for hollow cast- 
iron columns with both ends flat, when the length exceeds 
thirty times the diameter, the breaking weight equals the pro- 
duct of the 3 '6th power of the external diameter, in inches, 
less the 3 '6th power of the internal diameter, also in inches, 
multiplied by 44*34 (a coefficient deduced from the experi- 
ments) divided by the 17th power of the length, in feet. 

For columns with both ends rounded, or fixed by pins 
passing through the ends, ^rd of the above strength only 
should be reckoned upon, and for columns with one end flat 
and the other end round, f rds of the result by the above rules. 

The iron, from which the columns used in the experiments 
were made, possessed a crushing strength of 49 tons per 
square inch, and the coefficients should be increased or 
decreased, in the ratio of that strength, compared with the 
strength of the iron of which any other columns are made. 

It was also found by these experiments that, if columns 
with flat ends are less than 30 times their diameter in 
length, or if the ends be rounded and the length is less 
than 15 times the diameter, that they will be partly crushed 
as well as bent ; and their strength is ascertained as follows : 

First ascertain their strength as columns with the ends 
flat, by the rule for columns exceeding 30 times the diameter 
in length, or, if the ends are rounded, 15 times the diameter; 
then their real breaking strength will equal the product of 
the strength found as above, multiplied by the crushing 
strength of the material of which the columns are to be 
made, as ascertained by experiment, divided by the strength 
found as above plus f of the crushing strength of the 
material. 



202 



On the Strength of Structures. 



From the experiments carried out with solid wrought- 
iron columns, it appears that the strength of square pillars, 
which are long enough to be bent before the material is 
much crushed, varies nearly as the 3*6th power of the side 
of the square, the lengths being equal. 

The results of the experiments upon rectangular tubes of 
wrought iron are shown in the following Table, from which 
it appears that, in tubes of equal thickness, the strength per 
square inch of section of the smaller tubes is greater than 
that of the larger, the 4-inch square tube, '06 of an inch 
thick, giving S-6 tons per square inch ; the rectangular tube, 
8 inches x 4 inches, giving 679 tons per square inch ; and the 
8-inch square tube giving 5-9 tons per square inch of section. 

Result of Experiments made to ascertain the Resistance to 
Compression of Rectangular Tubes of Wrought Iron. 

TABLE XLI. 







Form of section. 




Rectangul 


ar 8 inches 


Square 8 inches 


Square 


4 inches 


Length of tubes 


x 4 inches. 


side. 


side. 


in feet and 
inches. 




























Strength 




Strength 




Strength 




Thickness 


per square 


Thickness 


per square 


Thickness 


per square 




of plates 


inch of 


of plates 


inch of 


of plates 


inch of 




in inches. 


section in 


in inches. 


section in 


in inches. 


section in 






tons. 




tons. 




tons. 


Feet. 


Inches. 














IO 


O 


— " 


— 


— 


— 


•03 


4'9 


2 


6 


— 


— 


— 


— 


•03 


5'5« 


IO 





•06 


679 


•06 


5'9 


•06 


8-6 


2 


4 


•06 


7-1 


— 


— 


— 


— 


IO 





— 




— 


— 


•083 


11-24 


2 


6 


— 


— 


— 


• — 


•083 


12-24 


IO 





— 


— 


•139 


91 


•134 


9-63 


7 


6 


— 


— 


— 


— 


•134 


io-35 


10 





— 


— 


•219 


11-84 


— 


— 


10 





•264 


I2'OI 


— 


— 


— 


— 



All these tubes failed by buckling or wrinklin 
plates. 



g up of the 



On Columns. 



203 



It will be seen also from Table XLL, that, to obtain twice 
the strength, four times the thickness of plate had to be 
used, whereas in some previous experiments on the crushing 
strength of wrought-iron plates, similar to a side of these 
tubes, the strength varies as the cube of the thickness. 

Result of Experiments made to ascertain the Resistance to 

Compression of Cylindrical Tubes of Wrought Iron. 

TABLE XLII. 







<o 


<o 





O 


s"° s 














In 4 " > U 


Pas 2 




Length 


£ t> 




£ ST « 


0$^ 




SK« 




in 
feet. 


w.a-- 


C 4)4 

gpr 




•2 « g> 

rt £ § 

-a 




a a. 2 
03 « 


Remarks. 


IO 








1 

80 




6-55 




5 


1-495 


•101 


•4443 


40 


15 


13-92 




2-5 








20 




15-27 




IO 

5 

2'5 


1-964 


•104 


•6104 


1 
60 

1 
SO 

15 


1 
19 


io-35 
i486 
i6- 5 


All sank by- 
flexure. 


IO 








JL_ 




13-29 


Sank by flexure. 


5 


2-49 


•107 


•8045 


1 

24 


1 
22 


15-67 




2-5 








12 




16-29 




IO 








1 




9-6 


Both sank by 


2'5 


2-35 


•242 


1-605 


1 
13 


1 
10 


14-78 


flexure. 


IO 








1 
40 




12-36 




7'5 


3-0 


•151 


i'349 


30 


20 


I3-3 




2-5 








1 
10 




167 


Slightly bent. 


IO* 

7'5 


4-o5 


•14 


17 


1 
30 

1 
22 


1 
29 


12-34 

14-88 


> Crushed. 


10 

7-5 


6-36 


•13 


2-54 


1 

¥ 

15 


1 
49 


16-02 
18-6 


"1 Failed by 
J crippling. 



204 On the Strength of Structures. 

It also appears that, in square tubes compressed to such a 
high degree, the length has little effect upon the strength, 
for in these experiments the io-feet tubes stood nearly as 
much as the 2 feet 9 inch tubes. 

It is obvious, from careful study of these tables, that 
wrought iron is unsuitable for columns, for in Table XLIL 
we see that columns only 12, 13, and 15 times the diameter 
sank by flexure, and in one case, where the length was only 
10 times the diameter, the column was bent, and in Table 
XLI. we find a 4-inch tube 2 feet 6 inches long, or only 
l\ times the side of the square, failed by the buckling of 
the plates ; and, in one case, a very short tube (1 foot 
7|- inches only), with a section of 8 inches x 4 inches and 
■06 of an inch thick, failed in the same manner, although 
the length was only 5 times the width of the least side. 
Still, columns are often made of wrought iron, and notably 
in the case of poles for sheer-legs, sometimes to over 
100 feet long, to lift 120 tons and upwards, and by using 
these tables of strength, and allowing such a margin that 
the breaking strength shall be 10 times the working load, 
and stiffening by internal X i f0n ribs or L irons, the struc- 
ture will be perfectly safe. 

To find the strength of a wrought-iron column, multiply 
its sectional area in square inches, by the strength per 
square inch given in these tables, for the column bearing the 
nearest relative proportion of diameter or side of square to 
length, and of thickness to diameter or side of square ; this 
will approximately give the strength of the column required. 

Steel is used in the present day, to some extent, for the 
poles of sheer-legs, and will no doubt in time supersede 
wrought iron for such purposes ; for it is equally safe, and 
combines with its safety a compressive strength superior to 
either wrought or cast iron, and is not nearly so liable to 
flexure as the former, nor to fracture as the latter. 

Some portable steel sheer-poles were recently constructed 
for the War Department to carry 18 tons on each pole, or 



On Columns. 205 

36 tons altogether, both when in a vertical position and, 
also, when fixed at such an angle that the top end is 15 feet 
from the vertical through the bottom end. These poles are 
40 feet long, 15 inches in diameter at the centre, and 8 inches 
at the ends, the thickness of plate being only -185 of an 
inch, the ratio of diameter to length being -£% at the centre 
and -g^o at the ends, and the ratio of the thickness to 
diameter -Jy at the centre, and ^ at the ends. 

The lower ends of these poles are fitted with ball and 
socket joints, in order to allow the necessary amount of 
lateral movement, and the blocks, which carry the weight to 
be lifted, are suspended from a pin, passing through the 
upper ends of the poles. Consequently these poles must 
be treated as columns with rounded ends, and they are 
only capable of' supporting ^ of the weight which similar 
poles, with ends flat and fixed, would support. 

This pair of sheer-poles was tested with a weight of 
36 tons, when in the inclined position of 15 feet out of the 
perpendicular, in which position a load of 36 tons is equal 
in effect to a load of 40 tons with the poles in the vertical 
position, and it produces a stress of 2-3 tons per square 
inch of section at the centre of the poles. This load they 
withstood, without the slightest perceptible deflection. 

It will be seen by reference to Table XLTI. page 203, that 
a cylindrical column of wrought iron with both ends flat, 
and a diameter equal to -^ of the length, and a thickness 
equal to -^ of the diameter, was crushed with 1 2 ^34 tons 
per square inch of section. 

The crushing strength of a similar wrought-iron column, 
with both ends rounded, would be ^ of 12-34 tons, or 
4*i 1 tons per square inch of section ; and, allowing the safe 
load of such a column to be \ of the crushing load, the 
working strength would be about 1 ton per square inch of 
section, or less than ^ the stress to which the above steel 
poles were subjected. 

This single example will serve to show that steel may, in 



206 On the Strength of Structures. 

time, be extensively applied with great advantage, in con- 
nection with such structures, and more particularly will 
this be the case, when they have to be transported from 
one place to another, and frequently dismounted and re- 
erected in an entirely different situation, because the whole 
of the gear, both for their transport and re-erection, would 
be proportionately lighter. 



CHAPTER XV. 

ON THE STRENGTH OF CRANES AND ROOF TRUSSES AS 
EXAMPLES OF COMPLEX STRUCTURES. 

When the student has mastered the preceding chapters 
upon beams and pillars, comparatively little difficulty will 
be experienced in understanding the present chapter, which 
treats of the strength of more complex structures. Most of 
the examples here given are chosen from actual works, which 
have recently been carried out in the War Department, and 
although some of them may at first appear difficult to 
understand, they are really simple, if the principles applicable 
to them are carefully studied. 

Before commencing to ascertain the strength of a struc- 
ture, the whole question raised should first be broadly and 
closely considered, in order to determine the direction and 
nature of the forces to which the structure may be exposed 
in its various parts. It will then be found that by far the 
larger proportion of these forces, in modern structures, are 
in the direction of the length of the parts of the structure, 
and even the majority of the transverse forces are so sup- 
ported, that they give rise to simple tensile and compressive 
strains, which act in the direction of the length of the com- 
ponent parts of the structure. It is comparatively rare to 
find parts exposed to forces which tend to rupture them by 
cross-breaking, as in the case of a beam. 



On Roof Trusses and Cranes. 



207 



This conversion of the direction of the strains is mostly- 
effected, by skilfully forming the structure of one or more 
triangles or systems of triangulation, or, in more familiar 
terms, by bracing the component parts of the structure. 

The triangular form of structure is now used, in preference 
to any other, simply because a triangle is the only figure 
whose shape cannot be altered, while the length of its sides 
remains constant. 

One of the simplest and most familiar forms of a braced 
structure is that of a common roof truss of small span, as 
shown in Fig. 24. It consists of two oblique rafters and a 
tie-beam ; the weight upon the entire truss is transmitted to 
the walls by the rafters, and the office of the tie-beam is to 
prevent the lower ends of the rafters from spreading out- 
wards, and thereby overturning the walls or columns sup- 

Fig. 24. 







porting the truss. Each truss has to support one bay of 
the roof, and consequently each of the two rafters has to 
support one-half of the weight of that part of the roof 
which lies between two adjacent trusses, and as this weight 
is uniformly distributed, it may be represented as if it really 
acted at one point ; namely, in the middle. The whole 
structure is balanced or kept in equilibrium, on each side, by 
three forces : first, the reaction of the wall, which is equal 
to one-half the weight upon the entire truss ; second, 



208 On the Strength of Structures. 

the oblique thrust of the rafter; and, third, the horizontal 
tension of the tie-beam. 

It is one of the fundamental principles of mechanics, that 
if three forces acting upon the same point are in equilibrium, 
then three lines, drawn parallel to the directions in which the 
forces act, will form a triangle, the lengths of whose sides 
are exactly proportional to the magnitudes of the forces. 
Hence, if three forces act at any point of a braced structure, 
the directions of which are known, we can determine their 
relative magnitudes by drawing a triangle. Further, if the 
magnitude of one of the forces is known, and the side of 
the triangle corresponding to that force is made equal to it 
in magnitude, on any scale of equal parts, then the other 
sides of the triangle will be equal to the other forces, on the 
same scale. 

Referring to Fig. 24, the triangle a b c is formed by 
drawing lines parallel to the directions of the acting forces, 
one of which passes along the oblique rafter, the other 
along the tie-beam, the third being the upward vertical re- 
action of the wall. As the weight upon the wall is the only 
known quantity, the student will first draw a vertical line 
a b to represent, on any convenient scale, the upward re- 
action ; that is to say, if the weight or upward reaction is 4-J 
tons, then the length of the line drawn must be made 4-J 
inches, or 4J half-inches, or 4J units of any other convenient 
dimension. From the ends of the line so obtained, let two 
other lines b c and a c be drawn, parallel to the other two 
forces, so that the three lines may form a triangle ; then the 
length of the sides of the triangle, when measured by the scale 
used for the vertical force, will represent the exact amount of 
the thrust upon the rafter and the tension on the tie-beam. 

The strains that come upon the diagonals of lattice girders 
and the more complicated forms of roofs may also be found 
in a similar manner, but the student is referred to the litera- 
ture specially devoted to those structures for further infor- 
mation. He is, also, advised to make himself master of 



On Roof Trusses and Cranes. 2C9 

the foregoing simple illustration of the truss, before going 
farther, because, when it is thoroughly understood, the re- 
mainder of the chapter will be found comparatively easy, and 
if it is not understood, to go farther will be useless. 

Fig. 25 is a skeleton diagram of the form of trussed beam 
used for overhead travelling cranes, for road and railway 
bridges of short span, and sometimes for the transverse 
girders of a bridge carrying three or four lines of rails. To 

Fig. 25. 






ascertain the strain upon the top beam of such a structure, 
which is generally of timber, find the weight acting at the 
centre ; multiply that weight by half the span of the truss, 
and divide by the depth of the truss, as in the case of the 
flanges of an ordinary beam. The stress upon the strut and 
tie-bar may be found, by drawing the triangle a b c, as ex- 
plained in the previous example. Let the beam be 20 feet 
span and required to carry 6 tons at the centre ; the depth 
of the truss is usually made -^th of the span, and in this 
example is 2 feet 6 inches. 

The strain along the top bar will be 10 x 6-7-2-^=24 tons. 
The compressive strength of timber may be taken at 6,000 
lbs. per square inch, and the safe working stress at T V tn °f 
that amount — namely, 600 lbs. — and the sectional area of 
material required will be the strain in lbs. divided by the 
working stress per sq. inch to be put upon the material ; 
thus, 24 x 2240 -r- 600 = 895. square inches. 

The strains upon the strut and tie-bar are shown by the 
diagram to be 8*54 tons on the former, and 3 tons upon the 
latter ; the weight upon each strut is equal to the total weight, 

p 



210 



On the Strength of Structures. 



divided by the number of points of attachment of the struts. 
If the load moves from one end to the other of the beam, 
or acts, as shown in Fig. 26, sometimes at one end and 
sometimes at the other, the truss must be counterbraced, 
as shown by Fig. 26 ; because, when the weight is over the 
strut a, the tie-rod a b c tends to straighten itself, and forces 
the other strut b upwards, and with it the beam ; this force 
is generally counteracted, in light crane beams, by putting 
sufficient material in the timber beam to make it stiff enough 
Fig. 26. 




to bear the stress without deflection ; but when used for 
heavy cranes, small bridges, or the transverse beams of large 
bridges, the' truss should be counterbraced, because the 
continual moving load would, otherwise, cause an incon- 
venient amount of deflection in the top beam, and at the 
same time would tend to rupture it transversely. 

The strains upon the tie and counterbraces are shown by 
Fig. 26, where the weight is directly over one of the struts; 
the downward pressure is resisted and balanced by the 
tension upon the tie-bar and counterbrace, and the strains 
are represented by the triangle a d e, whose sides are lines 
drawn paiallel to the directions of the forces, and as the 
line a e is made equal to the weight by scale, the other lines 
represent the magnitude of the other strains. 

The hydraulic wharf crane (Fig. 27) is another familiar 
example of the employment of a braced structure, the 
framing by which the top cap and slew drum are carried, 
forming one side of the triangle, and the tension rods and 
jib the other two sides. At the jib head three forces meet 



On Roof Trusses and Cr< 



anes. 



211 



and are in equilibrium — namely, the downward pull of the 
weight, the resistance of the tension rods, and the oblique 
thrust of the jib — and they may be represented by the sides 
of the triangle a be, Fig. 28, which are drawn parallel to 
them. If the side a b (which is drawn parallel to the down- 
ward pull of the weight) be made by scale to represent the 
v/eight, the lengths of the other sides a c and a b will repre- 



Fig. 27. 



Fig. 28. 




sent the tension upon the tie-rod and the compression upon 
the jib. In this case, with a weight of 6 tons, the tension is 
18 tons, and the compression is 2i-| tons, by scale. 

The crane post is subjected to a transverse strain caused 
by the oblique pull of the tension rods at its upper end ; 
the amount of this pull in the horizontal direction can be 
ascertained, by resolving the oblique pull into its two com- 
ponent parts, one horizontal or at right angles to the post, 
and the other vertical. This latter may be disregarded for 
the present, as it causes no transverse strain upon the post. 
This resolution may be made as shown on the upper part of 

r 2 



212 On the Strength of Structures. 

Fig. 28, in which ac represents the pull of the tension rods 
in direction and magnitude, dc the horizontal component of 
the pull of the tension rods, and da the vertical component. 

The post of this crane may be considered as similarly cir- 
cumstanced to a cylindrical or other beam, projecting from a 
wall and loaded with a weight at its outer extremity, equal 
in amount to the horizontal component of the oblique pull 
of the tension rods, as found by the diagram. It is also 
subjected to a compressive stress in the direction of its length. 

The compressive stress in the direction of the length of 
the crane post involves a more recondite calculation ; it will 
be found equal in amount to the weight of the crane 
structure, plus the effect of the weight lifted ; which latter 
will be equal to the algebraical sum of the vertical components 
of the oblique pull of the tension rods and the thrust of the 
jib ; that is to say, the vertical component of the former will 
act upwards upon the post, but that of the latter down- 
wards, and the resulting effect of these two opposite forces 
will be the remaining portion of the greater stress after the 
lesser stress has been subtracted from it, because the 
greater neutralises the lesser, and the remainder only acts 
upon the post. This force is comparatively so small that 
the calculation may be disregarded, because if the crane 
post is strong enough to resist the transverse strain, then 
the compressive strain will not be called into such exercise 
as will affect the stability of the structure. 

On the Strength of Sheer-legs. 

The sheer-legs, or poles, shown by skeleton diagram in 
Fig. 29, are an example of a temporary braced structure. 
In this figure b c represents the position of the sheer-legs, 
and a c that of the tension rod. The tension rod in this case 
is termed a ' guy,' and may be either a hempen or wire rope, 
or chain. The holdfast for this guy is furnished by strong 
pickets driven into the ground, and the thrust upon the 
poles is supported by a small foot plate, laid upon a platform 
of timbers at B. 



On Roof Trusses and Cranes. 2 1 3 

The diagram (Fig. 30) shows the method of ascertaining 
the strains upon the poles and the guy, by the triangle 



dr's* 



,'30 tons" 



214 O n ti ie Strength of Structures. 

of forces. With a 30-tons load, hanging 12 feet beyond 
the perpendicular, the thrust on the sheer-legs will be 
found to be 34-5 tons, and the tension on the guy ro*6 tons. 

The amount of the strain upon the guy may, however, be 
found by the principle of the lever, or, as it is sometimes 
called, the principle of moments, as shown by Fig. 29. 
The pole b c may be regarded as a lever turning upon b as 
a centre ; then the weight multiplied by the perpendicular 
distance at which it acts from b — in this case 12 feet — and 
divided by the perpendicular distance of the guy from b, 
will give the tensile stress upon the guy. The best method 
to find the length of the perpendicular from the fulcrum b 
to the guy is to make a skeleton diagram similar to Fig. 29, 
but to a scale of not less than 5 feet to 1 inch. 

The sheer-poles are 40 feet in length, the distance from 
the holdfast to the bottom of the poles is 120 feet, and the 
top of the poles is 12 feet beyond the perpendicular line 
raised from the centre of the feet of the poles ; with these 
data, the length of the perpendicular b d will be found 
to be 34 feet. Then 30 tons x 12 feet ~ 34 feet = 10*59 
tons, the strain on the guy rope a c. Although there are 
two guy ropes used with these sheer-poles, there is of course 
no strain upon the fore guy when the weight is in the posi- 
tion shown on the diagrams. 

The two guys are provided to enable the sheers to pick 
up a weight at the point shown on the diagram, and transfer 
it to the position shown by dotted lines, the strain upon the 
one guy rope gradually decreasing till the poles reach the 
perpendicular position, at which point there is no strain 
upon either guy ; but immediately that point is passed the 
other guy is subjected to a strain gradually increasing, until, 
when a point is reached 12 feet upon the other side of the 
perpendicular, it is of course strained to the same amount 
as the other guy was in the first position of the load. 

To permit this movement and to render it a perfectly 
safe operation, and also to enable a light hoisting crab, 



On Roof Trusses and Cranes. 215 

with its small complement of men, to perform the work, 
a portion of the guy is composed of an ordinary tackle, 
consisting of two blocks with three pulleys in each, and the 
necessary length of rope to allow the guy to be lengthened 
the required amount ; the running end of the tackle is wound 
direct upon the crab barrel. Then as the strain is distributed 
to six reduplications of the rope, the strain upon each of 
them and on the rope leading to the barrel will be only ^th 
of the total strain upon the guy, or io-6 — 6 = 176 ton. 

To enable the weight to pass between the poles, they are 
set 20 feet apart at the bottom • and if the hold fast ends of 
the guys are fixed on a line bisecting at right angles the 
line joining the feet of the poles, there will be no lateral 
strain upon the structure, except such as may be due to 
an external circumstance, such as a side wind, and which 
the spread of the feet of the poles enables them to resist 
effectually. 

On the Strength of a 30- Ton Steam Crane. 

Fig. 31 shows an arrangement of steam crane, for lifting 
weights of 30 tons, and as there are in the various parts of 
this structure examples of transverse, tensile, compressive, 
and shearing strains, it is selected as an illustration, to show 
the student a method of ascertaining the amount of the 
stresses upon such a structure, and also the quantity of 
material required to resist them. 

This crane works upon a centre pivot at b, and is pre- 
vented from rising by nuts, which act as a collar, and are 
fixed to the pivot in such a manner as to prevent un- 
screwing. 

The jib of the crane is upon one side, having two rollers 
which travel upon a circular rail at a, and is partly counter- 
balanced by the weight of the steam boiler, steam engines, 
and platform, but still leaving a weight of about 2 tons, so 
that the weight of the jib may be disregarded when the 
crane is unloaded. The steam power is used for lifting or 



2l6 



On the Strength of Structures. 



lowering, and is also employed for turning the crane round 
upon its pivot, by giving a slow motion to one of the rollers, 
and the apparatus is so arranged that the motion for raising 




On Roof Trusses and Cranes. 



217 



or lowering, and that for turning in either direction, may 
both be in gear at the same time. 

The whole crane structure is kept in equilibrium by three 
forces — namely, the downward pull of the weight, the re- 
sistance to the pressure upon the guide rail a, and the 
resistance to the upward pull upon the centre pin or pivot b. 
It may be treated as a large bent lever loaded at the end of 
one arm with a weight of 30 tons. 

The direction of these three pressures are shown in 
Fig. 33. The weight, multiplied by its perpendicular dis- 
tance from the guide rail or fulcrum of the lever, and 



Fig. 33. 




39-2 tons 



Fig. 34. 

divided by the length of the other arm of the lever, gives 
the amount of force that is acting at the short end of the 
lever, to balance the weight of 30 tons; thus, 30 x 25 -?- 
9-17 = 82 tons nearly, and this force of 82 tons, resolved 
(as shown by the diagram, Fig. 34) into its horizontal and 
vertical components, gives 39*2 tons for the former and 
72 tons for the latter. To find the pressure upon the 
guide rail, multiply the weight by its distance from the 
centre pivot, and divide by the distance from the other end 
of the lever to the guide rail; thus, 30 x 33 -=- 9*17 = 
108 tons. 



21 8 On the Strength of Structures. 

Having found the strain upon the centre pin and guide 
rail, and agreed upon the nature of the foundation best 
adapted for the situation, it becomes a simple matter to 
determine the amount of material necessary to resist those 
strains. 

The strains upon the jib and tension rods of the crane 
may be found by means of a diagram, in a similar manner 
to that described for finding the strains upon the same parts 
of the hydraulic wharf crane, and by reference to Fig. 32 
it will be seen that they amount to 77 tons compression on 
the jib, and 56 tons upon the tension rods, while lifting a 
weight of 30 tons, and the quantity of material required to 
resist the strains upon the tension rods, when the iron is 
subjected to a stress of 2 tons per square inch, will be 56 ~ 
2 = 28 square inches, and as there are two rods, there will 
be 14 square inches required in the section of each, and if 
the rods are round they will be 4^ inches in diameter. 

The jib of these cranes is a most important part of the 
structure, and the great compressive strength of cast ircn 
would seem to indicate that it would be the best material of 
which to construct it ; but there are many difficulties in 
making a cast-iron jib of such proportions, capable of with- 
standing with safety the shocks to which all crane structures 
are more or less subjected, in working, and hence wrought 
iron is used as it is more reliable. 

Long pillars of wrought iron have to be carefully braced 
to resist the tendency to flexure, and more generally is this 
the case when they are not perpendicular to the line of 
thrust, or when they are (as it is sometimes termed) 'bowed.' 

Fig. 36 shows an arrangement of wrought-iron pillar very 
commonly used for the jib of large cranes, and also for the 
piers of viaducts and other similar structures ; it consists of 
two side plates of sufficient area to resist the compression 
to which they are subjected, when well braced with lattice 
bars, dividing the long unsupported column into a number 
of short pillars, and keeping the side plates in a direct line ; 



FIG. 35 



On Roof Trusses and Cranes. 2 1 9 

Fig. 56. Fig. 37. 




220 On the Strength of Structures. 

two angle irons, extending the whole length of these plates, 
are riveted to their inner side, for the attachment of the 
lattice bars. 

The side plates of this jib are subjected to a transverse 
strain, along their whole length, tending to produce flexure, 
the value of which may be found by resolving half the 
direct pressure on the jib (because there are two side plates) 
into its two component parts, as shown on the diagram 
(Fig. 35), the one, acting along the line of the side plate, 
equal to 38*3 tons, and the other, at right angles to it, which 
is equal to a compressive stress of 3*6 tons. This latter is 
the force which tends to produce flexure, and it is to resist 
this strain that the lattice bars are inserted ; these bars are, as 
shown in Fig. 37, of a T section, 6 inches x 3 inches x J an 
inch, and have an effective area to resist tensile strains of 3^ 
square inches, after deducting the rivet holes at their end. 

The tensile strain upon these bars is also shown on the 
diagram (Fig. 36), and is found by resolving the transverse 
stress of 3-6 tons upon the side plates into two component 
forces acting in the direction of the lattice bars, and equal 
10 2*5 tons on one and 175 ton on the other. A simple bar, 
^}j inches x -V an inch, would have been sufficient to resist 
this strain, and therefore there must be some other reason 
for making them stronger and of a T section, and it is 
to enable them to prevent the deflection of one bar with- 
out the other, and thus to form the whole into a structure 
capable of resisting the compressive and transverse strains 
above described, and also the tendency to deflection, or 
1 sagging,' as it is sometimes called, engendered by its own 
weight. 

The jib and tension rods are connected at the jib head 
by a strong turned pin, which also carries the two chain 
pulleys ; this pin is subjected to a shearing strain at each 
end, equal to the pull upon one tension rod, and it should 
at least be of the same sectional area as the tension rod, 
and hence of the same diameter; the lower end of the jib 



On Roof Trusses and Cranes. 221 

is connected to the crane framing by two strong turned pins, 
fitting into the framing and the side plates of the jib, which 
are made thicker at this point, and also at the point where 
the pin at the jib head passes through them, and bored out 
to the exact size of the pin. These pins are very impor- 
tant parts of the structure, and should be well fitted, so that 
they cannot bend in the holes through which they pass. 

Each pin at the lower end of the jib has to resist a pres- 
sure of 38-5 tons — that is, one-half the total thrust — and, in 
order that the material may not be subjected to a greater 
stress than 2 tons per square inch, must have a shearing 
section of 38*5 -=- 2 = 19*25 square inches. But as the 
pin would have to be cut across at each side of the side 
plate, it need only have an actual sectional area of 19*25 ~ 
2 = 9*625, which is equivalent to a diameter of 3^- inches ; 
but if the pin is not supported at each side, it must then 
have an area of 19*25 square inches, as above stated, or a 
diameter of about 5 inches. 

Each tension rod is also connected by a turned pin to 
the top of the side frame of the crane, similarly to the 
lower end of the jib ; these pins are of course subjected to 
the same stress as the pin at the jib head, but, as they are 
supported at each side of the eye of the rod, they only 
require to have half the sectional area ; that is, 14 ~ 2 = 7 
square inches, or a diameter of 3 inches. 

The centre pin, or pivot, upon which the crane revolves, is 
fitted at the top end with a strong nut, shown on Fig. 33,which 
is screwed down to its bearing upon the girder in which the 
pivot works, and may be secured by a steel pin, passing 
through the pivot and nut, or otherwise, so that the latter 
cannot work back ; and the girder is bored truly and the 
pivot is turned to fit nicely, so that there may be no play. 
This pivot and nut have to resist the whole of the upward 
pull due to the 30-tons weight ; the magnitude and direction 
of this force and its vertical and horizontal components are 
shown on Fig. 34. The latter of these strains acts with a 



222 On the Strength of Structures. 

leverage equal to the whole length of the pivot, tending to 
break it across in a similar manner to that described in the 
example of the wharf-crane post ; and if the pivot is made 
strong enough to resist this stress, it will be of ample sec- 
tional area to resist the vertical stress, which causes only a 
tensile strain upon the material. 

The formulas generally given, to find the diameter of 
round bars of iron required to cany a weight in this manner, 
are founded upon two facts : first, that a bar of wrought 
iron i inch in diameter and 12 inches long, supported at 
each end and loaded at the centre, will break with a weight 
of about 2,000 lbs. ; secondly, that the strength of such bars 
varies directly as the cube of their diameter and inversely 
as their length. 

We know that a bar or beam, similar in every respect to 
the above, but supported at one end and loaded at the 
other, will only support Jth of that weight, or 500 lbs. ; and if 
a i-inch bar, 12 inches long, breaks with 500 lbs., a similar 
bar, 32 inches long, (the length of the centre pin) will 
only bear 500 x 12 ~- 32 = 187I lbs. Therefore, the 
centre pin would require to be equal in diameter to the 
cube root of its breaking weight, divided by 187-J, the 
breaking weight of a i-inch bar, or, which is the same thing 
put in another way, the cube of the diameter of the centre 
pin, must be equal to the breaking weight in lbs. which it 
will have to support, divided by 1S7I-. 

The breaking weight should be 392 tons — that is, ten 
times the working stress of 39*2 tons, and 392 x 2240-^-187^ 
= 4683— and the cube root of 4683 = 1673— say, 16J 
inches — the diameter of pivot required, if it did not fit the 
hole in the girder. 

By making the pivot to fit the hole in the girder exactly, 
the load upon the pivot would be distributed over its entire 
length, and its strength would thereby be doubled, and 
hence the cube of the diameter of the pivot required would 
be only one-half of that required under the former circum- 
stances. 



On Roof 1 russes and Cranes. 223 

The cube of the diameter in the former case is 46S3, 
and in the latter case would be 4683 divided by 2, which 
is equal to 2341*5, and the cube root of 2341*5 is 13*26 — 
say, 13^- inches — the diameter of pivot required, provided it 
is made to fit in the girder exactly. 

The sectional area of pivot required to resist the vertical 
component of the load only, supposing the material to be 
subjected to a stress of 2 tons per square inch, would be 
72 tons -f- 2 = 36 square inches, or an equivalent diameter 
of 6*8 inches nearly ; so that if sufficient material is provided 
to resist the lateral or transverse stress, there will be ample 
to resist the vertical or tensile stress. 

The cast-iron girder a, Fig. 33, in which the pivot is 
fitted, is 8 feet long between the supports, and 2 feet 
6 inches deep, and has to resist the same strains as the 
pivot — that is, a pressure at the centre of 72 tons, the verti- 
cal component of the upward pull of the crane, and, as 
previously explained, in the case of the common cast-iron 
girder at p. 175, the bottom flange will, by the principle of 
the lever, be subjected to a stress caused by half the weight 
upon the girder, multiplied by half the span, and divided by 
the depth of the girder — thus, 36 x 4 -*- 2 J = 56*4 tons, 
and allowing that cast iron in a crane structure should not 
be subjected to a tensile stress of more than 1 ton per 
square inch of section, the flange must contain 56*4 square 
inches of iron in its section : each flange has to resist the 
same amount of lateral strain, and it would therefore be 
advisable, in this case, to make them of the same sectional 
area at the centre, and reduce them each to §rds the area at 
the ends. 

The girder above the guide rail is cast hollow, so that the 
upper half of the guide wheels may work within it; the trans- 
verse section is shown in Fig. 39, and the side elevation in 
Fig. 41. This girder has to resist an upward force equal 
to the pressure upon the guide rail, shown by the diagram 
(Fig. 33) to be equal to 108 tons ; the top flange of this 
girder will be subjected to a tensile strain, because the load 



224 On the Strength of Structures. 

upon it acts vertically upwards, instead of downwards, as in 
the case of any ordinary weight. 

This girder is also 8 feet span and 2 feet deep, and it is 
loaded at two points ; namely, directly above each guide 
wheel at 2 feet from the ends, with a pressure at each point 
of half the total load, equal to 54 tons, as shown in Fig. 40. 
Each of these forces is equal in its effect upon the girder 
to 27 tons, acting at the centre of its length, because, 
although the weight is reduced one-half, its distance from 
the support, and consequently its leverage, is doubled, and 
a total force of twice 27 = 54 tons, acting at the centre of 
the girder, would be precisely equivalent to the two forces of 
54 tons acting as shown in the diagram. By a similar pro- 
cess to that pursued in finding the strain upon the flange of 
the girder a, we find, that this weight of 54 tons would cause 
a tensile strain of 54 tons upon the top flange of this girder — 
that is to say, the weight upon one support, due to the 54 
tons acting at the centre of the girder — namely, 27 tons, 
multiplied by half the length of the girder, 4 feet, and 
divided by the depth, 2 feet, = 54 tons— and therefore the 
sectional area required in the flange to resist it, when the 
iron is subjected to a stress of 1 ton per square inch — 54 
square inches. As there is no lateral strain upon this girder, 
the bottom flange may be reduced to ^th the area of the 
top, or 13^ square inches ; but as one-half of this flange will 
be placed on each side of the guide wheel, the webs should 
be connected by a cast-iron rib across the middle of the 
girder, as shown by the dotted lines in Fig. 40. 

The side frames of a crane are necessarily made of such a 
form as maybe best adapted to give room for the various bear- 
ings and supports for the connection ,of the jib, tension bars, 
and connecting girders. The principal stress, upon the side 
frames of these cranes, is that which is caused by the pull of the 
tension rods at the top, and these frames may be considered 
to be subjected to a similar strain to a wall crane, when lift- 
ing a weight at a distance beyond its proper radius, as shown 



Crane Gearing. 



225 



I08tons 




226 On the Strength of Structures. 

in Fig. 41, the horizontal members of these side frames being 
in a similar position to the wall upon which the crane is 
fixed, and the other members fulfilling the same office as 
the tension rod and strut of the wall crane, the pull of the 
tension rods of the large crane representing the weight. 

The total pull exerted by the tension rods is 56 tons ; 
that is, 28 tons at the top of each of the side frames. This 
force is balanced by the resistance to tension supplied by 
the vertical member, and the compression of the oblique 
member, and if, as before explained, lines are drawn parallel 
to the direction of the three forces, and the one representing 
the pull of the tension rod be made equal by scale to 28 tons, 
the length of the other lines, measured by the same scale, 
will represent the strains on the vertical and oblique mem- 
bers, as in Fig. 41. By the diagram, these forces are found 
to be 44 tons on the vertical, and 37 tons upon the oblique 
member of the frame, and hence an effective area, when all 
holes are deducted, of 44 square inches, will be required to 
meet this strain alone in the vertical member, and additional 
material to resist the load caused by the gearing shafts. 

The oblique member has, in addition to the compressive 
strain caused by the pull of the tension rods, to withstand 
the pull, at the centre of its length, of the hoisting chain 
upon the barrel, which amounts to 7 J tons, as. shown in 
Fig. 38. 

The shafts which carry the gearing of a heavy crane 
are of great importance, and the method of finding the 
diameter of shaft, required to resist the strains, can be best 
shown by a few examples ; we may take, for instance, the barrel 
shaft, and the shaft of one of the guide wheels, which is fitted 
with gear and driven to slew the crane round. The principal 
strain to which these shafts are subjected is that of torsion, 
and the torsional strength of cylindrical shafts varies as the 
cube of their diameters ; this knowledge, coupled with the 
fact that a bar of wrought iron 1 inch in diameter is twisted 
asunder by a weight of 800 lbs., acting at the end of a 



Crane Gearing. 227 

12-inch lever fixed upon one end, enables us to determine 
the size of shaft required to resist any torsional strain. 

The barrel shaft of this crane has to resist a twisting force 
of i\ tons, acting upon a barrel 4 feet diameter, the length 
of the lever being one-half the diameter or 2 feet, and the 
breaking strength of the shaft should be equal to ten times 
that amount, or 75 tons acting with a 2 -feet leverage. The 
breaking strength of a i-inch bar with a 2-feet lever will 
be 800 -J- 2 = 400 lbs., and hence by dividing 75 tons 
reduced to pounds by 400, we obtain the cube of the 
diameter of shaft required. Thus 75 x 2,240 -r- 400 = 
420, and the cube root of 420 = 7*488, say 7^- inches, the 
required size of shaft. 

The load upon the guide-wheel shaft is determined by 
the adhesion due to the weight upon the wheel, which under 
favourable circumstances amounts to 600 lbs. per ton of the 
load, the weight upon the wheel is 54 tons, and 54 x 600 
= 32,400 lbs. as the adhesion of the wheel upon the guide- 
rail. The diameter of the wheel is 3 feet, and therefore the 
length of lever 18 inches; the weight required to break a 
i-inch bar with 18-inch lever = 800 x 12 -~ 18 = 533 lbs. 
The breaking strength of the shaft should be ten times the 
adhesion acting at the end of an 18-inch lever, that is 
32,400 x 10 = 324,000 lbs., and 324,000 -f- 533 = 608, the 
cube of the diameter of shaft, and the cube root of 608 = 
8*47 inches, the diameter of shaft required. 

The size of the remaining shafts is determined in the 
same manner, that is, by first finding the twisting load, then 
the strength of a i-inch bar under the same conditions, 
dividing the former by the latter and extracting the cube 
root of the quotient. 

Referring to thwemarks made at page 185, on the com- 
parative strength of shafts with overhung gear, and to 
gear having an outer bearing, let us apply them in such a 
crane as that now under consideration. 

Let us suppose the pinion which gears into the wheel 
Q 2 



228 On the Strength of Structures. 

on the barrel shaft, namely, the main driving pinion of such 
a crane, to be keyed upon the outer end of a shaft, say 
4 inches in diameter, and that the pinion is 12 inches wide 
and has to drive the large spur wheel, with a load of 7 J tons 
at the pitch line. We have already said, that a bar of 
wrought iron 1 inch in diameter and 1 foot long, supported 
at both ends, will be crippled with a weight of 2,000 lbs. 
acting at the centre. Now a similar bar, supported at one 
end only, and having the load distributed as in the case of 
the above shaft, would only support one-half of 2,000 lbs., 
or 1,000 lbs., and as the strength of cylindrical beams varies 
as the cube of their diameters, all other conditions being 
the same, the above-mentioned shaft would be crippled 
with a weight of 1,000 lbs. multiplied by the cube of its 
diameter, or 1,000 x 64 = 64,000 lbs. The actual load 
on the shaft is 7 J tons, or 16,800 lbs., and hence the ratio 
of the working to the breaking stress is, as 16,800 is to 
64,000, or as 1 is to 3*8. 

Such a margin of safety, although sufficient for many 
purposes, is not so in the case of a crane. The breaking 
strength (as has been several times stated) should be at 
least ten times the working load, to ensure perfect safety. 

This margin of safety is more especially required when the 
load is being lowered, under the control of the friction break, 
and then suddenly checked ; the effect of the load, in conse- 
quence of the stoppage of the motion, is increased to an ex- 
tent which may imperil the whole fabric. 

This margin would be more than obtained, by simply 
increasing the length of the 4-inch shaft, and putting a 
bearing outside the pinion instead of having it overhung, 
as the breaking stress of a i-inch bar, under these altered 
circumstances — that is to say, when supported at both ends 
and with the load distributed — would be 2,000 x 2 = 
4,000 lbs., and hence the strength of the given shaft would 
be 4,000 x 64 = 256,000 lbs., and the ratio of the breaking 
strength to the working-load would be as 256,000 is to 
16,800, or as 15 is to 1. 



Crane Gearing. 229 

Although, when the pinion is overhung, the arrangement 
may not necessarily cause the breaking of the shaft directly, 
still it will permit it to deflect and thereby cause the load 
to be thrown upon one end of the tooth, namely, upon 
that which is next to the bearing, instead of upon the 
whole length as it ought to be, and will thus endanger the 
safety of the gearing ; and even if this latter should be of 
ample strength, the deflection of the shaft will continue, 
until in time the. shaft will take a permanent set, and ulti- 
mately break off, close to the bearing. 

The method of finding the strength of the teeth required 
in the respective wheels has been explained in Chapter XIII., 
p. i87. 

Having thus far shown how to find the quantity of 
material required in the various parts of the crane, we have 
now only to deal with the chain for carrying the weight, 
and by general consent the Admiralty formula given at p. 153 
is adopted. 

In these cranes the weight or load upon the chain barrel 
is diminished, by multiplying the number of chains to carry 
the required weight. The total weight of 30 tons is sup- 
ported by four chains, thus : The chain is anchored to the 
underside of the jib-head, and passes down under one of 
the pulleys in the movable block, up to and over a pulley 
at the jib-head, and again descends, passes under the 
second pulley in the movable block, and finally ascends 
and passes over a second pulley at the jib-head and thence 
to the barrel, 

The load on each of the lengths of chain above the 
movable block will, therefore, be 30 tons -^4=7! tons. 

Another way of finding the strain on the chain, which 
may be used when there is any exceptional arrangement of 
the blocks or tackle, is to see how much chain is taken up 
in lifting the weight 1 foot ; then if, as in this example, 4 feet 
of chain are taken up on the barrel, the load upon the chain 
will be ^th of the total weight lifted 3 if 6 feet be taken up, 



230 On the Strength of Structures. 

the load will be £th, and so on ; for, by a well-known princi- 
ple, a small weight acting through a long distance is pre- 
cisely equal to a large weight acting through a proportion- 
ately shorter distance. 

On Crane Foundations. 

In order that such cranes may be reliable, it is necessary 
to have a sound and unyielding foundation. Where the 
ground is firm and solid, there is comparatively little diffi- 
culty in obtaining the required stability, but, as a rule, in 
the places in which cranes have to be erected, it is other- 
wise. To meet the requirements fully, the foundation should 
be such, that the pressure on the guide wheels does not cause 
the guide rail to yield perceptibly, as it passes round the 
circle ; a yielding rail adds considerably to the motive power 
required to turn the crane round. 

In Figs. 42 to 49 are shown three descriptions of founda- 
tion, which have been constructed for 30-ton cranes. The 
foundation illustrated in Figs. 42 and 43 is adapted for a 
crane situated upon an ordinary solid wharf; that in Figs. 
44 and 45 is for a crane which had to be erected at some 
distance from a wharf, in order to obtain a sufficient depth 
of water to allow vessels of the larger class to come under the 
crane. From the isolated position of this crane, sufficient mass 
had to be placed in the foundation to render it perfectly 
stable and capable of resisting any strain tending to overturn 
it, without throwing any strain upon the light jetty, erected 
to carry the loads to and from the crane. The foundation 
shown in Figs. 46, 47, 48, and 49 is for a crane erected at 
the head of a long pier. 

In each of these three descriptions of foundation, sufficient 
weight or resistance is provided in order to counterbalance 
the upward pull of the centre pin, on which the crane turns, 
and also for any increased strain that might be caused by 
the sudden stoppage of the descending weight, which is the 
chief cause of accidents. Hence, although the actual strain 



Crane Foundations. 



231 




Fig. 42. 



«Q» 






:-:c: 
a.'V'.'S: ' 





^ '^J IvJ **« i/v/i W 

Section 

Fig. 43. 



•> ** 



232 On the Strength of Structures. 

is 82 tons, the weight or resistance of material which would 
have to be lifted, before the crane could overturn, is 328 tons, 
or four times the amount of the ordinary working strain. 

Concrete is used in two of the foundations (Figs. 43 and 
45) to furnish the necessary weight, and the cast-iron block, 
in which the centre post is fixed, is secured to the mass by 
means of four holding-down bolts a a, each bolt being fixed 
to a strong cast-iron plate 6 feet square, which is embedded 
in the bottom of the concrete mass, and drawn up tight by 
strong nuts fitted upon the upper end of the bolts. 

In each case, these holding-down bolts have to resist an 
ordinary working load of 82 tons (Fig. 33), and as they may, 
by the carelessness of the breaksman, have to resist a much 
greater strain, they should not in ordinary working be called 
upon to bear more than 2 tons per square inch of their sec- 
tional area, when each bolt will have to resist a vertical 
strain of 72 tons -=- 4 = 18 tons, as will be seen by Fig. 34. 
This vertical strain, in consequence of the oblique position 
of the bolt, produces on it a tensile strain of 19 tons, and 
therefore they must each have a sectional area of 19 -=- 2 = 
9 \ square inches (the stress per square inch to which the 
iron is to be subjected being 2 tons). To obtain 9^ square 
inches of section, the diameter must be 3-^ inches nearly ; the 
actual diameter of the bolts used was 4 inches. 

The second class of foundation (Figs. 44 and 45) depends, 
entirely, upon its mass for stability. It consists of a cast-iron 
cylinder 20 feet in diameter, and 36 feet high, filled up to 
within 5 feet of the top with concrete, the remaining space 
being occupied by masonry to form a bed for the centre 
block and guide rail ; the total weight of the cylinder, its 
contents, and the crane, is 690 tons, and a force equal to a 
weight of 300 tons, hanging from the crane-hook, would be 
required to balance it ; for, by taking moments about the 
bottom edge of the cylinder, we have on the one side 690 
tons multiplied by 10 feet, and upon the other 300 tons 
multiplied by 23 feet, each of which equals 6,900. Hence 



Crane Foundations. 



233 




Fig. 44. 







1 ". » - >' '■=•». • n . - • *■'. ■•; ■ "' 
;•;.-- ■* Con.cretG « »* , ! 

Section 



Fig. 45. 



234 On the Strength of Structures. 

the whole structure is just balanced ; any excess of weight 
above the 300 tons, upon the crane, would overturn the 
whole foundation. 

Before erecting such a mass, the bottom upon which it is 
to be built should be carefully examined, and if it is not 
sufficiently hard to resist the weight, it must be piled, as 
shown in the wharf foundation, Fig. 43 ; in the case of the 
cast-iron cylinder foundation, the bottom was solid rock, 
and consequently quite able to resist the pressure, which 
amounted to 2*3 tons per square foot of surface. 

In the construction of a large cast-iron cylinder, much 
judgment is required. A comparatively weak cylinder would 
suffice, after it is erected and filled in with concrete, but the 
dangerous period in its histoiy is during the time of its erec- 
tion, when it is empty and subject to the pressure of a rising 
tide, tending to crush it inwardly by a collapse of the fabric. 
To meet this, the joints of the plates ought to be broad and 
planed, so as to have a uniform bearing, and to fit all over 
the surface, in order that the arch, formed by the cylinder, 
may be rigid. The reason of this will be more apparent to 
the student after reading the next chapter, where reference 
is made to the collapse of steam-boiler flues, and the laws 
by which they are governed. 

In the third class of foundation, shown in Figs, 46, 47, 
48, and 49, which has been erected at a pier-head, the con- 
ditions are more complicated, and will require some attention 
to enable them to be understood. 

The centre support consists of a cast-iron cylinder, seven 
feet in diameter. This cylinder is carried down to the solid 
gravel, and is filled with concrete. The top of this cylinder 
is made to receive the lower ends of the four holding-down 
bolts, a a. It will be evident that this centre pillar would 
be insufficient of itself to furnish the necessary stability, not 
only in consequence of its want of breadth of base, but 
likewise on account of the great intensity of the pressure at 
the base. It will be seen, by referring to Fig. 47, that a 



Crane Foundations. 



235 



Fici. 46. 




Fig. 47. 



236 



On the Strength of Structures. 




Fig. 48. — Plan on Lower-tier Girders. 

o = =0 ==& 




Fjg. 49. — Plan on Upper-tier Girders. 



Crane Foundations. 237 

portion of the weight of the foundation of the pier crane 
structure is thrown upon the eight surrounding piles, each 
of which is fitted with a screw blade si f eet in diameter. 
These eight piles have therefore a bearing surface of 80 
square feet, and together with the 7 -feet cylinder represent 
a bearing surface of 118 J square feet. 

The wrought-iron guide rail, upon which the crane re- 
volves, is laid upon a strong cast-iron ring or girder, and the 
load is transmitted from it to the central cylinder and the 
surrounding piles, by twelve cast-iron struts ; eight of these 
struts rest upon the central cylinder, and the remainder upon 
the lower tier of girders and against the four corner piles of the 
surrounding square. The strains upon these struts are shown 
in Figs. 50 and 51. The weight upon the guide rail is 108 
tons, distributed by the two guide wheels or rollers, and it 
is supported by at least two of the central struts in any 
position of the crane ; and when the crane is directly over 
one of these struts, one half of the load is carried by the 
two adjacent struts, and the other half by the strut directly 
under the centre of the crane ; hence the greatest load upon 
either of the struts is equal to 108 -=- 2 = 54 tons of ver- 
tical pressure. 

These struts are in a similar position to the jib of a crane, 
and the pressure upon them may be found by a triangle of 
pressures a be (Fig. 50), as explained in the example of the 
wharf crane. The amount of this strain is shown by the 
diagram to equal 56 tons, and as the length of the strut is 
only about eighteen times its least breadth, it may be sub- 
jected to a stress of 1 J ton per square inch of its sectional 
area, at the centre of its length, with safety ; and the sec- 
tional area required at the centre will be 56 -r- ij = 37J 
square inches. The actual form of section is shown in the 
figure, and the actual area is equal to 39! square inches. 

When the crane is directly over the diagonal of the square 
formed by the surrounding piles, the vertical pressure of 54 
tons is supported by one central and one diagonal strut, 



238 On the Strength of Structures. 




Fig. 50. 



Section 




Fig. 51. 



Crane Foundations. 239 

and the strains upon each are shown, by the diagram a b c, 
(Fig. 51) to equal 33 tons on the former and 24 tons on the 
latter. 

The weight of the crane and its foundation, including the 
cast-iron cylinder filled with concrete, is about 190 tons ; this, 
with the weight lifted, is equal to a total of 220 tons, a por- 
tion of which is transmitted to the surrounding piles by the 
eight diagonal struts, already referred to, abutting upon the 
underside of the lower tier girders, and fixed at their lower 
extremity to the piles, by a joint pin 3 inches in diameter. 

These eight struts have each to support a vertical pressure 
of 220 ~ 8 = 27^ tons ; and as they rest upon a joint pin 
at one end, they are only capable of carrying frds the load 
of a similar strut with both ends fixed, and therefore must 
not be subjected to a greater stress than 1 ton per square 
inch of sectional area at the centre. By diagram, as shown 
in Fig. 53, the longest struts, namely those fixed to the 
corner piles, are subjected to a compressive stress of 33^ 
tons by the action of the vertical pressure of 27-J tons upon 
the upper end, and hence the sectional area required is 33^ 
square inches. The actual form of section is shown in 
Fig. 52, and it has an area of 36 square inches. 

If the student has been able to understand this chapter, he 
will be in a position to apply the knowledge acquired in other 
directions. The elementary principles here explained are 
not by any means confined to the examples that have been 
selected for illustration ; they are equally applicable to a 
variety of other structures. The remarks that have been 
made, upon the direction and amount of stress which is 
brought to bear upon the members of roofs and cranes, relate 
also to any other structure in similar circumstances, and it 
will be useful for the student to apply the knowledge gained 
in other cases with which he has to deal, so as to fix the 
principles in his mind. The same may be said of the obser- 
vations on form and proportions, and on the quantity of 
material to be introduced so as to afford the requisite 



240 



On the Strength of Structures. 



strength, that the structure may not only be able to balance 
the stress, but to have in addition the necessary margin of 
safety. The margin of safety necessary in different cases is 
a subject which admits of great difference of opinion ; in this 




Fig. C2. 




Fig. 53. 

volume a leaning to extra caution has been chosen with a 
purpose, so that if the student errs at the outset of life, he 
may err on the safe side ; and as he gains experience, the 
margin of safety can be modified if it is found advisable. 



241 



CHAPTER XVI. 

STRENGTH OF RIVETED STRUCTURES— STEAM BOILERS, ETC. 

Built-up structures, such as steam boilers, which are made 
of thin plates, riveted together by clenched iron rivets, 
depend for their strength upon a number of conditions. 
As a rule, the boiler plates have not the same ultimate 
tensile strength, per square inch, in the direction of the fibre, 
as the same iron when made into the form of thick bars. 
The difference amounts even to several tons, and still more 
unsatisfactory is the reduction of strength in the other, or 
transverse direction. This limited tenacity in boiler plates 
is no doubt due to the rolling of the plates to such thinness, 
but the weakness must be recognised in estimating the con- 
ditions of strength in a steam boiler. 

In the chapter on wrought iron, it will be seen that from 
23 to 25 tons, per square inch, is the usual tensile strength of 
such a quality of wrought iron as is required for this pur- 
pose ; but when this quality of iron is made into thin 
boiler plates, the tenacity is frequently reduced to 20 or 
21 tons, and is seldom over 22 tons; and in the other, or 
transverse direction, it is rarely over 19 tons per square inch 
of sectional area. 

An important practical lesson to be drawn from this cir- 
cumstance is, that the boiler-maker, in arranging the order 
of the plates for the construction of a boiler, should have 
their strongest direction put in the line of the greatest stress. 
Take, for example, the shell of an ordinary cylindrical 
boiler; the least strain is in the direction of the length, 
hence the strongest direction of the plates should be put 
circumferentially. This is also the better arrangement, on 
account of the greater extension or wire-drawing that the 
iron will submit to, when it is drawn or stretched in the direc- 

R 



242 On the Strength of Structures. 

tion of the fibre. For reasons to be shown hereafter, boilers 
are seldom found to give out in the direction of the length, 
from constructive weakness ; that is, if they are sufficiently 
strong in the other direction, namely, circumferentially. 

When these boiler plates are joined together by the usual 
butt or lap joints and riveting, the joint becomes still 
weaker than the plates across the fibres. In thus joining 
the plates together, by a butt or lap over and rivets, the 
strength will obviously depend on the resistance both to 
shearing and to tearing. The rivets may be considered as 
pins which may be shorn, the force which is required to 
shear a rivet being the shearing strength of the iron, per 
square inch, multiplied by the sectional area of the rivet. 
The tearing of the plates may occur in two ways, either 
by the plate tearing along the line of rivet holes, or from 
the pieces between the hole and the edge of the plate being 
forced outwards, by the simple detrusion of the stronger 
rivets, the force required being as the shearing strength per 
square inch, multiplied by the area of the pieces thus 
pushed out of place. 

The shearing strength of rivets depends on the quality of 
the iron, and ranges from nearly 23 tons, in the very best 
descriptions, down to \Z\ tons; but 22 tons per square inch 
is usually considered to be about the average strength of 
the best Yorkshire iron suitable for rivets. The iron of the 
best plates is about the same in quality as that of the rivets, 
and, in the direction of the fibre, may be considered to have 
a tenacity of 22 tons per square inch. 

In order to have the rivets equal in strength to the plates, 
it is necessary to observe a definite proportion between the 
diameter and pitch of the rivets and the thickness of the 
plates. The usual rule is to make the diameter of the rivet 
equal to two thicknesses of the plate, which, as regards 
strength, is a small fraction under the correct equivalent, 
but is sufficiently near for all practical purposes. 

The plates at the lap or butt being double, will be about 
equal, in strength, to the rivet, if the space between the hole 



Strength of Riveted Structures — Steam Boilers, &c. 243 



and the edge is equal to the diameter of the rivet ; hence a 
single riveted joint has a breadth equal to three diameters 
of the rivet, and the pitch, or distance from centre to 
centre of rivets, is three diameters. From this it will be 
seen that one-third of the metal has to be cut out of the 
plate, and its strength is thereby reduced one-third. This 
diminution of strength may also be aggravated by punching 
and rough usage in putting the plates together for riveting ; 
the tenacity of plates, originally 22 tons, may thus be brought 
down to 18 tons, but this may be avoided by piercing the 
hcles with a drill. 

The following Table is taken from the Proceedings of the 
Mechanical Engineers, for 1 872 ; it forms part of a paper which 
was read by Mr. Walter R. Browne, bearing on the subject of 
riveted structures, containing the results of experiments made 

by Mr. Kirkaldy. 

TABLE XLIII. 

Riveted Joints. 



Description of 
joint. 


Riveting. 


Rivet 
holes. 


Proportions. 


Ratio of 
strength 
of joint 
to that 
of plate, 
per cent. 


Diameter 
to thick- 
ness. 


Lap or 
cover to 
diameter. 


Pitch 
to dia- 
meter. 


Lap 

Lap 

Butt, 1 cover 
Butt, 1 cover 
Butt, 2 covers 
Butt, 2 covers 


Single ] 

Double j 

Single | 
Double] 

Single j 
Double ) 

1 


Punched 
Drilled 

Punched 
Drilled 

Punched 

Drilled 

Punched 

Drilled 

Punched 

Drilled 

Punched 

Drilled 


2 
2 

2 

2 

2 
2 
2 
2 

T i 

1 4. 
T i 

A 


Lap. 

3 

3 

Chain. Zig. 

5^ 6 
5 51 

Cover. 

6 

6 

11 12 

10 11 
6 

6 

11 13 
10 12 


3 

2§ 

41 

4 

3 

4 

4 

3* 

3 

51 

41 


55 ! 
^2 

[ 

69 

75 

55 
62 
69 
75 
57 
67 
72 
79 



244 Jl the Strength of Structures. 

The resistance to shearing is increased by the frictional 
force, arising from the grip, clue to the contraction of the 
hot rivet in cooling, and to the action of the hammer or 
riveting machine. This frictional adhesion is very con- 
siderable, but when added to the resistance to shearing it 
does not make the joint equal in strength to the plate, even 
in its weakest direction, which should be noted. 

From a number of valuable experiments, made by Sir W. 
Fairbairn, it appeared that, assuming the strength of the 
plate to be ioo, the strength of an equal length of the single 
riveted lap joint would be 56 ; but by having a double row 
of rivets applied, either to form zigzag or chain riveting, 
the strength was increased to 70. Putting it in another 
form, and assuming the strength of the iron to be 50,000 lbs. 
per square inch, then the strength of various kinds of riveted 
joints would be as under — 

lbs. 

Iron .... 50,000 'i . • 

Double riveted joint . 3 5,coo ^ S ^ Y& mch ° f the 

Single riveted joint . 28,000 J section of the P late " 

The reduction of strength due to riveting greatly affects 
the construction of boilers. The joint is evidently the 
weak link of an important chain ; consequently the strength 
of the boiler is only equal to that of the joints ; the greater 
strength of the plates is so much useless metal, which it is 
the object of the engineer to eliminate, so far as he may be 
able to do so, by the practical devices which are at his 
disposal. This may be done either by increasing the 
strength of the joints, so as to bring them up to that of the 
plates, or by reducing the substance of the remainder of 
the plates, or otherwise, the desideratum being uniformity 
of strength throughout the entire boiler structure. 

Since the above facts were made known, a considerable 
amount of attention has been directed to the subject, in 
order to devise some arrangement, whereby the strength of 



Strength of Riveted Str lectures — Steam Boilers, &c. 245 

the joint might be brought up to that of the plate. With 
this object in view, it has recently been suggested, to 
strengthen the joints of boilers and other riveted structures 
by modifying the shape of the rivet. Rivets are usually 
round, and about f-inch in diameter ; if, however, the same 
quantity of iron was made into an oval form, with the thick- 
ness of the narrow part J inch, the remainder of the metal 
going to increase the length in the other direction, the 
strength of the joint would be altered for the better, because 
a larger area would be left between the rivet holes. 

The resistance to shearing of an oval rivet will be pro- 
portional to its area, and will be nearly alike in either 
direction, as will be seen by referring to the chapter on 
shearing, p. 143. It is there shown that greater stress was 
required to shear a bar when placed on its edge than when 
laid upon its side, but it is more than probable that the 
increase of resistance was due to the shorter period occupied, 
in the performance of the operation, in the former case, 
with shears in which the blades were not perfectly parallel. 
This conclusion is supported by the general result of the 
experiments made on shearing and punching, which go to 
show that the stress required is as the area of surface which 
has to be detruded. 

With the boiler plates the case is different, because the 
weakening of the plates is in proportion to the area punched 
out, in the line of fracture through the rivet holes ; therefore, 
if a rivet, with the same strength as a f-inch cylindrical rivet, 
can be put into a hole which is only half an inch wide, 
measured along the joint, it is evident that, so far as this 
part of the joint is concerned, the plates would be made 
stronger by one sixth, all other conditions remaining the 
same. At the same time the rivet can be strengthened to 
{lie same extent, by increasing its substance in the longer 
dimension, so as to make the plates and rivets equally 
strong at the point of junction, so far as the resistance to 
shearing depends on the sectional area. But here another 



246 On the Strength of Structures. 

condition must be taken into account ; a very narrow rivet 
acts injuriously on the plate, consequently the limit of this 
narrowing of the rivet is soon reached, because when it 
becomes too thin, its wedge action comes into play with 
greater force, from want of the necessary breadth of bearing 
surface upon the plate, on the same principle that the 
diameter of the bolt or pin of a tie rod requires to be of 
larger sectional area than the rod itself, or that the double 
rope sling over a crane hook does not afford the double 
strength of two single ropes, which it always does when 
passed over a pulley of proper diameter, thereby avoiding 
the wedge action, due to the concentration of force upon a 
small bearing surface. 

Should such an arrangement of rivets be found to give 
satisfaction, there will be no practical difficulty in carrying 
out the system ; an elongated hole can be punched as 
easily as a round hole ; nay more, an oval hole can be 
drilled as easily and as cheaply as a round hole, when 
proper appliances are provided. This latter statement may 
be doubted by those who are only familiar with the piercing 
of holes of the round shape, but such is the case, neverthe- 
less, and as more refined systems of manufacture are in- 
troduced, and the forms given to boilers are simplified, the 
whole row of oval slits may be made at the same time, by 
a corresponding number of revolving chisels, the plate 
meanwhile having the requisite amount of transverse motion 
to give the elongation. 

The arrangement of joint-construction is also being modi- 
fied for the better in other directions. By looking at the 
section of a joint of the best form, when the ends of 
one plate or of two plates butt, and are riveted to one 
cover-plate, it is evident that the rivet is not in the best 
condition to do its full duty, that it would be stronger 
If there were two cover-plates, one situated as at present, 
only a little thinner in section, and having a corresponding 
one placed on the opposite side of the joint, thus supporting 



Strength of Riveted Structures — Steam Boilers ,&c. 247 

the rivet at both ends, like the links of a pitch-chain, and 
thereby adding to its efficiency. 

By referring to page 244, it will be seen that the strength 
of single riveting is to that of double riveting as 28 is to 35 ; 
hence, in the construction of the better class of boilers, the 
joints that have to resist the greater stress — that is, the 
circumferential stress — are double riveted, while those that 
have to resist the longitudinal or lesser strain are made with 
single riveting ; yet even the double rivets are relatively the 
weaker for their work, because the circumferential stress is 
doubly as great as the longitudinal stress. And when all 
has been done by these modifications, the joints are weaker 
than the original plates, to the extent of one-fifth of the 
strength of the plates. 

With the view, therefore, of raising the strength of the 
joints to that of the plates, Sir W. Fairbairn introduced the 
system of rolling the plates with a thicker substance at the 
edges, where the holes have to be pierced, so as approxi- 
mately to bring up the sectional area between the rivet 
holes to that of the general section of the plate, and 
thereby to obtain uniformity of strength throughout. 

Another most ingenious device which has recently been 
proposed is, to arrange the boiler-plate joints diagonally, 
instead of longitudinally and transversely, according to the 
usual method ; by the new system the shell of the boiler is 
formed by winding the plates in a diagonal or spiral 
direction, whereby the difference of strength in the two 
directions is considerably modified for the better. With this 
arrangement the joints are at an angle of 45 with the axis 
of the boiler, and the strength of the joints in the weakest, 
that is, the circumferential direction, is thereby consider- 
ably increased. 

Mr. W. R. Browne says that, ' taking the angle of the 
joints at 45 °, and considering any square portion of the 
boiler surface of which the joint forms a diagonal, it will be 
seen that, instead of the two pairs of equal and opposite 



248 On the Strength of Structures. 

tensions, one pair double in amount of the other pair, 
which would act on the sides of the square in ordinary 
square jointing, there are, with the diagonal jointing, two 
equal and opposite resultant tensions acting across the 
diagonal joint. The resultant tension, per inch run of the 
joint, is found on calculation to be about four-fifths of the 
greater tension, and it acts not exactly at right angles to 
the joint, but at an angle of about 72 with it. The latter 
circumstance, however, does not materially affect the result, 
and the tension on the diagonal joint may, therefore, be 
taken at four-fifths of that on the longitudinal joint ; con- 
sequently the effective strength of the joint and of the 
boiler is increased in the ratio of four to five. Thus, in a 
punched lap joint, if single riveted, the proportionate 
strength of joint as compared with that of the entire plate 
is increased from 55 to 69 per cent., and if double riveted 
from 69 to 86 per cent. The diagonal joints have, in most 
cases, to be replaced by transverse seams at the ends 
of the boiler; but as the tension on a transverse joint is 
only one-half of that on a longitudinal one, this does not 
form any objection.' 

The great change which has taken place in the manufac- 
ture of plates by the rolling process, whereby they are pro- 
duced of great length, breadth, and thickness, is leading 
rapidly to a simplification of the forms given to boilers, and 
to an increase of strength at the same time. The circular form 
of boiler is now employed for marine purposes, where 
rectangular boilers, with flat stayed surfaces, were formerly 
used, and are even yet employed in many cases. This 
modification, combined with elongated rivets, diagonal 
riveting, thickened edges, and double cover-plates, will 
increase the strength of the structure at its weakest points, 
and render the strength more nearly uniform. 

The strength of a boiler is also much affected by the 
mode of putting the plates together, previous to riveting. 
When the holes are punched by careless workmen, it is not 



Strength of Riveted S true hires — Steam Boilers, &e. 249 

uncommon to find them not opposite to each other when 
the plates are brought together, and in order to be able 
to introduce the rivet, a taper-drift or punch is driven in, 
with violence, by means of a heavy hammer, thus damaging 
the line of holes to an incalculable extent, by sheer thought- 
lessness. In the construction of the best class of boilers, 
the specification provides that tne holes are to be drilled, 
and if any error is found to exist in the correct meeting of 
the holes, no drift is to be employed, any metal that has 
to be removed being drilled or rymered out with a cutting 
instrument, thus avoiding injury to the metal. 

The strength of boilers depends upon the nature of the 
material employed for their construction : wrought iron is 
that which is most generally adopted, but steel is now 
rapidly coming into use, and in past times copper was not 
uncommon. Stated in even numbers, the strengths of the 
three kinds of material stand to each other about as 
follows : — 

Steel 90,000 lbs. 

Iron . 50,000 ,, 

Copper ....... 34,000 ,, 

From this comparison, it may be correctly inferred that 
steel will be very generally used for boilers in the future. 

The strength of iron boilers is not much affected by 
the working temperatures, up to considerably over 400 , 
nor by low temperatures down to the freezing-point. But 
when the temperature of the plates, through the absence 
of water or any other cause, rises much above 500 , then 
a change commences. Above 750 the tenacity diminishes 
very rapidly, and when the plates become red hot, they have 
lost fully the half of their usual strength. 

In those parts of steam boilers where the pressure acts 
upon the exterior surface of tubes, as in the internal flues of 
the cylindrical boiler before referred to, new conditions are 
established. Here the tendency is to crush, and to cause 



250 On the Strength of Structures. 

a failure by collapse of the tube. To resist external pressure 
the circular is obviously the strongest form, and, conse- 
quently, it is that form which is now always preferred 
wherever it is admissible. In such constructions, lap-joints 
are avoided, and welded-joints are generally substituted, 
although sometimes the ring is made in one or two pieces 
with butt-joints and cover-plates, to which the ends of the 
rings are riveted, either with single or double riveting. 

The greatest tendency to weakness, in such flues, arises 
from the difference of expansion and contraction, due to the 
changes of temperature that are likely to arise in ordinary 
working, thus causing a difference of length between these 
flues and the exterior shell of the boiler : hence many plans 
have been resorted to, in order to give the different parts 
some freedom to act, according to their several require- 
ments ; one of the best is that shown in Fig. 54. 

This diagram represents part of the internal flue of a 
cylindrical boiler, such as is shown in Fig. 57 ; the tubular por- 
tions marked a a a a in the diagram are made by bending 
a plate into an overlapping circle, and then the ends are 
wielded into a perfectly cylindrical, but short tube, of the 
breadth of the boiler plate. These short tubes are then 
joined by means of rivets, in the usual manner, to the corru- 
gated rings or hoops, b b ; the left-hand part of the diagram 
shows the exterior of the flue, while the other part shows it 
in section, from which it will be perceived, that the curved 
form of the ring gives the flue considerable liberty to 
expand and contract, as may be necessary, during the 
lengthening or shortening that takes place in the ordinary 
working of the boiler, but which would 'not be the case 
if the ring was made of a J_-iron or other solid form, or 
even if the flue were of one piece. This hollow form which 
is given to the ring likewise secures another important 
advantage, inasmuch as it allows the entire substance of the 
flue to be of nearly uniform thickness, or rather thinness, 
because so far as the transmission of the heat and the 



Strength of Riveted Structures — Steam Boilers, &c. 251 

endurance of the material are concerned, the thinner the 
flue, the better it is. Another advantage arises from the cor- 
rugated shape, in that it becomes a sort of circular beam 
to prevent the collapse of the flue. 




Fig. 54. 

This arrangement of flue construction, therefore, not only 
affords liberty of motion in the direction of the length, but 
at the same time it adds greatly to the strength of the flues 
in resisting collapse, at the edge of each plate. From 
certain experiments, made by Sir W. Fairbairn, the marked 
superiority of circular to elliptical or other forms of tube, in 
resisting collapse, was most decided, and where strength 
combined with thinness are of such importance, the circular 
form should not be willingly departed from. 

In order to make sure of the strength of steam boilers, 
when in ordinary use, the best practical course is to subject 
them to a hydraulic test, periodically, say after every 500 
hours of actual work. The pressure applied should be the 
double of that to which the safety valve is ordinarily loaded, 
or one-third of the ultimate strength of the structure. There 



252 On the Strength of Structures. 

is no risk of danger arising from this test, and if only a 
moderate degree of intelligence is brought to bear upon the 
boiler, during the process, in order to watch its behaviour, all 
risk of an explosion from weakness is avoided, and the 
operation is accomplished at a cost so trifling as not to be 
worth regarding, when valuable life and property are at 
stake. Belonging to the War Department, there are about 
two hundred steam boilers, which are all treated as here 
recommended, and hitherto with the most satisfactory re- 
sults. 

From these general remarks, it will be seen that the 
strength of steam boilers depends on many conditions, but 
if the exact conditions are precisely known, then there will 
be no difficulty in estimating the strength, as due to form, 
dimensions, quality of material, and workmanship. 

To enable the student to understand the nature of the 
strains in steam boilers, a few simple examples are here 
selected, for his guidance in the investigation of these and 
other similar structures. 

Previous to estimating the strength of steam boilers, it is first 
necessary to examine and consider their shape, and the direc- 
tion of the strains to which they are exposed. Let us select, 
as a simple illustration, the case of a plain cylindrical boiler, 
with hemispherical ends, as shown in Figs. 55 and 56. This 
boiler is exposed to rupture in two directions, as shown by 
the arrows, first from the ends being pushed asunder, which 
is resisted by the iron contained in the transverse sec- 
tion of the shell ; second, by the bursting the cylindrical 
shell in the direction b b, which is resisted by the iron con- 
tained in the substance of the shell, when considered as a 
ring. This latter strain is similar to that in a water-pipe, 
and consequently the stress is as the diameter of the pipe or 
boiler, that is to say, a boiler of double diameter would 
necessarily require to have double the thickness of iron to 
give the same strength, whereas in the other direction, 
although the surface exposed is as the square of the diame- 



Strength of Riveted Structures — Steam Boilers, &c. 253 

ter, yet for certain reasons, which will be presently stated, 
it is still the stronger. Let us suppose this boiler to be 
20 feet long, by 54 inches in diameter, and that it is con- 
structed with plates of wrought iron of three-eighths of an 
inch in thickness. The strength in the direction a a de- 
pends on two conditions : first, the greatest sectional area 
which is exposed to the pressure, namely, the diameter 
squared and multiplied by 7854, which is equal to an area 
of 2290 square inches \ second, the resistance offered by an 
entire ring of the iron of the shell, taken in the transverse 
direction, which in this case will be 54 x 3-1416, equal to a 
circumference of 169-64 inches, the thickness of the iron 
being three-eighths of an inch. 

Here an important question arises, namely, What is the 
ultimate strength of the shell per square inch of section? 
The ultimate strength of the iron may be 50,000 lbs. per 
square inch. But the shell is weakened by the riveted 
joints which connect the plates together. 

Suppose that the joints are double -riveted, the rivets being 
placed in a zigzag direction, so as to obtain the best result. 
Then the tenacity of the joint may be taken at 35,000 lbs. 
per square inch of the gross section of the plate, as has been 
already mentioned. For a single-riveted joint, we should 
have had to reduce the strength to 6,000 or 7,000 lbs. per 
square inch less. To allow an ample margin of safety, we 
will assume the strength of the double-riveted joint to be 
34,000 lbs. per square inch. 

The length of the ring of the shell is 169*64 inches, the 
thickness is fths of an inch, therefore 169-64 x fths x 
34,000 will give a total resistance equal to 2,162,400 lbs. ; 
then if we divide that strength, by the area of the section of 
the boiler, we shall have the pressure per square inch that 
would be required to burst the shell in the longitudinal 

direction ; 2,T 2 '4°° _ g^ ib s# ultimate bursting pressure 

area 2290 
per square inch. 



254 



On the Strength of Structures. 







fsi 



* 




< -P 



) 



Strength ofR iveted Structures — Steam Boilers, &c. 255 

As regards the strength in the other direction b b, let us 
suppose a ring in the middle of the shell, one inch in length, 
this ring will be exposed to a certain pressure per inch, on a 
surface of 54 square inches, with an amount of iron to resist 
that force equal to twice f x 1, or jths of a square inch. 
Then, taking the strength of the weakest point, as before, 
34,000 lbs. x| = 25,500 lbs., the resistance of the ring, and 
this divided by the area of 54 square inches will give a total 
resistance of 472 lbs., which is exactly the half of the 
strength in the other direction. The lesson is here taught, 
that the shell is twice as strong in the direction a #, as it is 
in the direction b b, for a given uniform internal pressure. 

The ultimate strength at the weakest point is thus equal 
to a pressure of 472 lbs., and the boiler would be perfectly 

safe if worked at 60 lbs. steam pressure, so that ^^=7-86, 

60 

showing that it would have a margin of safety fully 7 J times 

the working pressure, which, however, is not by any means 

too much for a new boiler, because corrosion and other 

causes will soon reduce the original strength. 

To select another familiar example, that of the ordinary 

flat-ended cylindrical boiler, with two internal flues, passing 

from one end of the boiler to the other end, and both riveted 

to the flat ends, as shown in Figs. 57 and 58. Here the 

conditions are widely different to what they were in the 

former example. In considering the extent of surface which 

is exposed to pressure at the two ends of this boiler, it will 

evidently be necessary to deduct the area of the two flues, 

and, still farther, in reckoning up the quantity of iron which 

resists pressure in that direction, it will be equally necessary 

to take the tensile strength of the iron, composing both the 

shell and the two flues, which together will place the strength 

of the ends in a still higher ratio to that of the shell, in a 

longitudinal direction, than in the case previously considered. 

There is one weak point, however, in these flat ends — 

namely, at the point marked a in Fig. 58; this arises from 



256 On the Strength of Structures. 

the flatness of the form and the thinness of the plate. If 
the ends were hemispherical, which is the strongest form, 
then it would be different. Still, for convenience, they are 
flat and hence weak at the point a, and therefore have to 
be supported, either by tie-rods passing from end to end 
of the boiler, or by what are termed ' gusset-plates/ b b, as 
shown. These are plates combined with angle irons, which 
are riveted both to the shell and to the upper part of the 
flat ends. 

The course to pursue, in finding the strength of this shell, 
would be exactly the same as in the former example, because 
the shell is not assisted by the flues. Suppose, then, the 
boiler to be 7 feet in diameter, by 28 feet long, with two 
flues, each 30 inches in diameter, and for convenience let 
us suppose the iron to be \ an inch thick throughout, 

then M = 404 lbs. as the bursting pressure per square 

84 x 1 

inch of the shell. The strength of the ends will depend 

upon the area exposed to pressure. 

84 x 84 x 7854 = 5542 = whole area. 

30 x 30 x 7854 x 2 = 141 3 = flue area to be deducted. 



or 4129 inches of surface exposed to pressure. 

The circumference of shell equals . . 264 inches. 
Do. do. of the two flues . . 1 88 , , 



452 „ 

of J-inch iron, which is equal to 226 square inches, 

in strength, 34,000 lbs. per inch; then ^4 _ 

4129 

i860 lbs. as the ultimate pressure' per square inch, which 

would be required to rupture the boiler transversely, thus 

showing that this boiler is fully four-and-a-half times as 

strong to resist the longitudinal pressure, as it is to resist 

the pressure which tends to rupture the shell in the other 

direction. 



Strength of Riveted Structures — Steam Boilers, &c. 257 

But here it has to be remarked, that such boilers, or, 
indeed, boilers of any other shape, may be weakened to 
any extent by improper arrangements, as, for instance, by 
cutting out holes for the steam-dome, or manholes, without 
introducing material to counteract the loss of strength thus 
occasioned. The judicious boiler-maker will always in- 
troduce strengthening rings, or otherwise stiffen the part 
affected, in order to fully make up for the weakening 
of the general structure, due to the cutting away of the 
material. 

There is another important practical point, which affects 
to a considerable extent the endurance of steam boilers, 
namely, the arrangement of the plates that have to be 
joined. This remark applies more especially to the shell 
and the flues of boilers of the cylindrical shape. For- 
merly, it was usual to unite the shell and flues to the end 
plates by means of an angle iron, but the better mode is to 
flange over the iron plate, in order to shorten the distance 
between the rivets and the point of exposure to pressure, 
and thereby to reduce the leverage of the stress which tends 
to open the joint. The same general remark applies to the 
system of overlap joints, either in the shell or the flues ; 
there is more ' work ' or stress thrown upon them than is 
the case when the shell is more perfectly cylindrical, with the 
shell-plates butted to each other, and then united by cover- 
plates. By this arrangement the strain is more direct, and 
anything that reduces the tendency to movement contributes 
to the permanence of the boiler. 

When a boiler structure is so combined that certain parts 
are kept in a state of restlessness, either through differences 
of expansion and contraction, or by having purts of the 
steam engine attached to different points, all such restless- 
ness tends to wear out the parts so exposed, not so much 
by the mere friction, as by a process of disintegration, 
whereby the incipient oxide is prematurely scaled from the 
surface of the plates or joints. 



258 On the Strength of Structures. 

We may select a third example of boiler, still more com- 
plicated, namely, the tubular variety, of which the boiler of 
the locomotive engine may be considered as the most 
familiar type. As the present purpose, however, is not to 
explain boilers, but rather to consider their strength only, 
let us for convenience take this boiler in its simplest form, 
as consisting of a fire-box #, barrel b, and smoke-box c, 
as shown in Figs. 59 and 60. A slight examination of 
its several parts will convince the student, that its three 
divisions are under very different conditions as regards 
strength. 

To select the cylindrical barrel first, because it corre- 
sponds more nearly to those boilers which have been 
already considered, the strength of the cylinder or barrel 
portion will be exactly the same as that of the shells of 
the two former examples, and therefore need not be further 
investigated. The small tubes likewise may be disregarded, 
because other conditions interfere, which demand for them 
a substance that places them far beyond the danger of 
collapse. 

The fire-box consists of two boxes, an internal and an 
external, and the whole of their parts, as well as the partition- 
plate of the smoke-box, are all most disadvantageously placed 
as regards resistance. They are thin flat plates of iron or 
copper, which, if left unsupported, would yield with a few 
pounds of pressure ; and when considered as a beam, with 
the load uniformly distributed, the strength of these plates 
to resist either breaking or deflection or collapse, from the 
great pressure of steam, may be set down as approximately 
nil, in consequence of the want of depth, due to the thin- 
ness of the plates. 

To those who are not familiar with steam boilers, the 
suggestion may occur, that this difficulty could be overcome 
by making them thicker, but such a course is impracticable 
on account of the plates of the fire box (which is the most 
vulnerable part) having to transmit the heat of the furnace 



Strength ofR ivcted Structures — Steam Boilers, &c. 259 

to the water, as rapidly as possible, so that it becomes 
necessary to resort to other means of strengthening, in order 
to have the whole boiler structure of equal strength, and 
without requiring or employing an inordinate quantity of 
material to accomplish this condition. 




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Fig. 60. 



Looking at Figs. 59 and 60 it will be seen that the steam 
or fluid pressure is acting upon all their flat surfaces, and 
tending to push the inner fire-box into the furnace, and the 
plates of the outer box outwards. Both are equally loaded 

s 2 



260 On the Strength of Structures. 

with fluid pressure, on every inch of exposed surface, and 
necessarily in opposite directions. This pressure, in opposite 
directions, is directly counteracted, and the two thin plates 
are united into one beam, by means of a series of copper or 
iron stays, these stays being repeated at every few inches of 
surface. The stays are inserted in such a manner as really 
fits them to take hold of the plates, with a grip equal 
to their own strength ; the plates are evenly drilled through, 
a suitable tap is employed to screw them both, at the same 
time, then the stay or bolt is screwed through both, and 
afterwards riveted over at each extremity, thus taking a 
double hold of both plates. Hence, the question of strength 
is transferred from the plates to the stays ; these stays are 
made of iron or copper, according to the class of boiler. 
Selecting the weaker metal, copper, for an example, let us 
suppose its ultimate strength to be 15 tons per square 
inch, and that we are disposed to put a stress upon it equal 
to 3 tons per square inch, which is as much as is suitable, 
and let us assume also that a stay is introduced to every 
25 square inches of surface, and that each stay has an area 
equal to the half of one square inch, this will give us a 
resistance of 1^- ton to be distributed over 25 square inches, 
or 134 lbs. per square inch, in addition to the modicum of 
assistance derived from the plates themselves. As such 
a boiler would not be worked at a pressure over 120 lbs. 
per square inch, it will be seen that the margin of safety is 
very considerable. 

The crown of the inner fire-box is a part which is much 
exposed to the fire, and stands out in a solitary position 
away from external support. We saw, in reference to 
copper, p. 79, that its strength does not improve when heated, 
on the contrary, it becomes weaker ; hencej the crown-plate, 
taking everything into account, is badly situated. In this 
strait, recourse is had to a series of thin beams on edge, or 
_L-irons variously applied, which are placed on its upper 
surface, and at regular distances apart, and to which the 



StrcngtJi ofR iveted Structures — Steam Boilers, &c. 261 

crown-plate is either stayed, or held up by ordinary rivets ; 
the stays or rivets being of such dimensions and number as 
will give the required resistance. The united strength of 
these beams, together with that of the stays attached to the 
top of the outer box 5 must be at least equal to six times 
the entire pressure which comes upon the crown. 

Here another difficulty occurs : the presence of such 
beams or J_ -irons necessarily interferes with the passage of 
the heat from the fire to the water, which is not only 
damaging to the metal, but is disadvantageous in other 
respects. To obviate this objection, the beam or _L-iron 
does not rest upon the crown all over, but is separated from 
it, either by distance-washers, or by relieving the under sur- 
face of the beams, or by other arrangements, so that the 
water is in contact with a surface of thin metal, which is 
prevented from deflecting by stays or rivets, that derive their 
support from an extraneous source, and the amount of 
resistance may be calculated in the same manner as for the. 
copper stays of the two fire-boxes. 

From several causes, the crown of this inner fire-box is 
more critically situated than any other part, and is more lia- 
ble to be weakened by the action of the fire ; its temperature 
is always greater than that of the water, which is still farther 
aggravated by the rapid formation of steam-bubbles, which 
form a medium between the hot metal and the body of solid 
water over it, so that in determining the strength of such a 
vital part, all these points must be taken into account, and 
due allowance made for the tear and wear, daring the period 
which it may be expected to last. 

The partition of the smoke-box and the corresponding 
part of the inner fire-box are exposed to the same fluid 
pressure as the other parts, just referred to, and as they are 
thin they would have, if left to themselves in that position, 
comparatively little strength. As a rule, however, they are 
thicker than the other plates, not from choice but from 



262 On the Strength of Structures. 

necessity, inasmuch as they have to hold a series of small 
tubes, through which the fiery gases pass from the furnace to 
the chimney. Hence, advantage is taken of these tubes to 
contribute assistance to the tube plates, by offering resistance 
to the fluid pressure as an additional duty. Corresponding 
holes are formed in both plates, the tubes, nicely prepared, 
are securely inserted, and as additional aid, ferrules (ac- 
curately fitted) are driven into the interior of the ends, 
thus converting the tubes into stays. 

It so happens, however, that these stays are not to be 
entirely relied upon, inasmuch as they are apt to work 
loose in the course of time. Hence, other more permanent 
stays of solid metal are introduced, at intervals, with nuts on 
the outer surface of both plates, thus rendering the structure 
more reliable. 

From the foregoing remarks on boilers, the student will 
perceive that the question of strength is not so difficult as it 
appeared at first sight ; it has only to be taken in detail, the 
various strains carefully worked out, and the strength of the 
material which is, or which has to be provided to meet the 
stress, may be calculated. 

Resistance to Collapse. 

The flues and other parts of boilers, which are exposed to 
the steam pressure acting from without inwards, tend to give 
way in another manner — by collapse. The flues are the 
most vulnerable part of the cylindrical boiler, unless they 
are properly supported, either by the corrugated rings already 
referred to, or by some other arrangement. The subject of 
collapse is so important that it is desirable that it should 
receive some further explanation. 

This most important subject was thoroughly investigated 
by Sir W. Fairbairn, who carried out a long series of ex- 
periments upon wrought-iron tubes at the request of the 
Royal Society and the British Association, the object being 
to ascertain the laws which govern the resistance to collapse 



Strength of Riveted Structures — Steam Boilers, &c. 263 

in such structures. The results have been freely published 
in Sir W. Fairbairn's 'Useful Information for Engineers.' 
As these experiments were extensive, the following brief 
remarks on the subject are only intended to describe the 
most important of the results which were obtained, and 
likewise to draw attention to some of the more important 
laws deduced from the experiments. 

In these experiments, the tubes were firmly secured at 
the ends, so as to be in the same condition as flues in 
steam boilers, and the end fastening probably contributed 
in some degree to the remarkable results obtained in these 
experiments. 

By these experiments it was shown, first, that with tubes 
of the same diameter and the same thickness of metal, the 
strength to resist collapse was nearly inversely as the length ; 
and, second, that with tubes of the same length and thick- 
ness, but of different diameters, the strength is nearly in- 
versely as the diameter. 

In the most important series of these experiments, the tubes 
were all cylindrical and of the same thickness, but varied 
in length and diameter. The tubes were made from a single 
plate, bent to the cylindrical form, and the joints riveted 
and brazed to render them water-tight ; the ends of the tubes 
were riveted to rigid cast-iron discs, and the air from the 
interior of the tube was allowed to pass out, when the tube 
collapsed, through a pipe screwed into one of the discs. 
The tubes were placed in a strong cast-iron cistern filled 
with water, and the pressure was applied by a hydraulic 
pump, and its amount was registered by two gauges of the 
best description. It is to be noted that the term collapse, 
as here used, does not imply the crushing of the material, 
but simply that the circular or elliptical arched shape of the 
transverse sections changes its form, at the weakest part of 
the tube, by the thin plates either bending or wrinkling. 
The results of this set of experiments are shown in the 
following Table : — 



264 



On the Strength of Structures. 



Results of experiments made to ascertain the resistance 
of cylindrical tubes of wrought iron to collapse when the 
ends are firmly fixed, and the tubes are subjected to an ex- 
ternal pressure. 



I 


2 


TABLE XLIV. 
3 4 5 


6 


7 


Number of 
the experi- 
mental 
tube. 


Size of the tubes. 


Mean pres- 
sure in lbs. 
per square 

inch at 
which the 

tube 
collapsed. 


Compara- 
tive num- 
bers show- 
ing the 
collapsing 
pressure 
reduced to 

unity of 
length and 
diameter. 


Mean of 

comparative 

numbers. 


Diameter 
in inches. 


Length 
in feet. 


Thickness 
in decimals 
of an inch. 


1-2-6 

3 
4 

5 
27 
29 


4 


T 7 

31 

31 

5 

5 

Z 2 


•043 


I49 
65 
65 

43 
47 
93 


930 

866 
823 
860 
940 
930 


8 9 I-5 


IOII 

9 


6 


411 


•043 


58-5 
32 


877 
944 


9IO-5 


i 13 ! 2 j 

i .5 ! | 3J 


•043 


39 
32 
3i 


780 

832" 
826 


812-6 


* IO % 


•043 


19 

33 


791 
825 


§08 


18 
19 

20 


12-2 


4al 

5 

2§ 


'043 


11 

'12-5 
22 


654 
75o 
660 


688 


i 

22 

23 
24 


18-75 


5^ 
3^ 
3& 


•25 


420 

262 
378 


40031 

7270 

10489 





Strength ofR ivetedStructu res — Steam Boilers, &c. 265 

It has to be noted that the experimental tube No. 6, 
although it was really 5 feet long, yet had two rigid cast- 
iron rings soldered upon it, dividing it into three equal parts, 
19 inches in length between the rings, and hence this tube 
is placed in the table with the tubes whose real length was 
19 inches. The result shows that, although the tube was 
really the same length as Nos. 5 and 27, it yet possessed 
three times the strength to resist collapse, a result which 
was due solely to the tube being kept in the true circular 
form by the cast-iron rings, and thus made virtually into 
three short tubes instead of one long tube. 

There are two great lessons taught by this set of experi- 
ments. 1 st. The resistance of tubes of uniform thickness 
varies inversely as the length, or nearly so. This law is 
clearly shown by the experiments, and by comparing the 
4-inch tubes Nos. 5 and 27 with No. 29. It will be seen 
that the former, which are twice the length of the latter, 
collapsed with about half the pressure, and Nos. 1 and 2, 
which were rather less than one-third the length of Nos. 5 
and 27, bore rather more than three times the pressure. 

The 6-inch tubes also follow the same law; Nos. 10 and 11 
collapsed at 58*5 lbs. pressure, and No. 9 should have borne 
a proportionate pressure, as due to its length, which may be 
calculated thus ;-— 59 inches : 30 inches : \ 58-5 lbs. : 2974 
lbs. But the actual collapsing pressure of the latter tube was 
by experiment 32 lbs., so that the difference between the 
calculated and actual pressure was only 2\ lbs. per square 
inch, which is very slight. 

The resistance of the 8-, 10-, and 12-inch tubes also bears 
the same relation to the length, and hence it may be con- 
cluded that the strength of such tubes, to resist an external 
pressure, varies inversely as the length, at least between the 
limits of 1^- and 10 feet. 

The furnace or flue tubes of steam boilers, at the time of 
these experiments, were made without any support between 
the extremities,, but an alteration speedily followed, so soon 



266 On the Strength of Structures. 

as the knowledge gained by these experiments was made 
known to the world. At the present time, the tubes of all 
well-constructed steam boilers are strengthened by rings 
of a X section, or of a corrugated section, these rings 
being riveted to the tube at intervals of about 3J feet, and 
this has added greatly to the security of boilers. 

The second lesson taught by these experiments is, that 
the resistance of such tubes to collapse, when the length 
and thickness are the same, varies inversely as the diameter. 
As an example, take No. 29, a 4-inch tube 2\ feet long, 
with a collapsing pressure of 93 lbs. per square inch, as a 
standard. Then, by calculation, the 6-, 8-, 10-, and 12-inch 
tubes of the same length and thickness should collapse with 
pressures of 62, 46-5, 37-2, and 31 lbs. per square inch 
respectively. By experiment, the pressures were found to be 
5^*5, 39, 33> an d 22 lbs. per square inch. 

The column No. 6 is composed of numbers obtained, by 
multiplying the collapsing pressure of the tubes by the 
length and diameter of the tube, to show how nearly the 
resistance of tubes of the same thickness is inversely pro- 
portional to their diameter and length ; and, had the tubes 
followed this law exactly, the numbers in that column would 
have been equal. The greatest discrepancy occurs with the 
12-inch tubes. 

The differences in these numbers, and likewise between 
the calculated and experimental collapsing pressures, may 
be accounted for, by the varying strength of the material and 
differences of workmanship, and, in the case of the 12-inch 
tube, by the difficulty of making so large a tube of such thin 
material, so that it may be perfectly cylindrical in all parts. 

The experiments Nos. 22, 23, and 24 in this Table were 
made with three tubes having a greater thickness in pro- 
portion to their diameters. Two of these tubes were pre- 
cisely similar in all respects, but that the one was made 
with a 'lap' joint (Fig. 61), and the other with a 'butt' 
joint and external cover plate (Fig. 62). 



Strength ofR iveted Structures — Steam Boilers, &c. 2 6y 

These experiments were made to ascertain, first, to what 
extent the strength of the tube was reduced by the slight 
departure from the true circular form, which is unavoidable 
when a ' lap ' joint is used; and secondly, to ascertain, if 
possible, the different powers of resistance of thick tubes of 
different diameters. The result- of the experiments shows 
that a loss of rather more than one-third of the strength 
was caused, by the slight deviation of a quarter of an inch 
from the true circular form in the 'lap '-jointed tube; 
this should be carefully noted. 

In well-constructed boilers, any deviation from the true 
form is avoided by making the tubes in short lengths, and 




Fig. 6i. Fig. 62. 

Map-welding' the joint, care being taken that the thickness 
of the tube is maintained, but not exceeded, at the weld. 
The cylindrical form is further secured by the strengthen- 
ing rings, which are now rolled out of the solid ' bloom,' 
and are therefore weldless and perfectly cylindrical, so 
that any departure from the proper cylindrical form is 
inexcusable. 

The resistance of the above three tubes was found to be 
much greater than that of those having a less thickness in 
proportion to their diameter, and Sir W. Fairbairn concludes 
that the strength of tubes of the same length and diameter, 



268 



On the Strength of Structures. 



but of different thicknesses, varies as the 2 -19th power of the 
thickness. For all practical purposes and to facilitate calcu- 
lation, the square of the thickness may be used instead of 
the more correct 2 -19th power, so that with two tubes 
precisely similar in every respect, but that the one is 
twice the thickness of the other, the strength of the former 
to resist collapse will be very nearly four times that of the 
latter. 

In all the foregoing experiments, the ends of the tube 
were securely fixed, and further experiments were made to 
ascertain whether similar tubes follow the same law, when 
the ends are left perfectly free. Two tubes were used for 
these experiments, they were 8 inches diameter and 30 and 
60 inches long respectively, the result is shown in the fol- 
lowing Table : — 

Result of experiments made to ascertain the resistance of 
cylindrical tubes of wrought iron to collapse, when the ends 
are perfectly free to approach each other, and the tubes are 
subjected to an external pressure. 





TABLE XLV. 




Number of experi- 
mental tube. 


Size of tubes. 


Pressure in lbs. 

per square inch at 

which the tuljes 

collapsed. 


Diameter in 
inches. 


Length in 
feet. 


Thickness in 

decimals of 

an inch. 


25 
26 


Y 


5 

2± 


} '043 


22 
36 



It appears from this Table that the strength is not in- 
versely as the length, as was the 'case when the ends of 
the tubes were fixed, or the shorter tube should not have 
collapsed until the pressure reached 44 instead of 36 lbs. 
per square inch. 

Comparing these experiments -with No. 13 in Table XLIV., 
it will be seen that a similar tube to No. 26, but with the 



Strength of Riveted Structures — Steam Boilers, &e. 269 



ends fixed, collapsed with 39 lbs. pressure, so that it appears 
that the freedom of the ends to approach each other does 
not decrease the strength to any considerable extent, pro- 
vided the circular form is still retained at the ends of the tube. 

'The next experiments were made with tubes of an elliptical 
form of section ; the result is shown in the following Table : — 

Result of experiments made to ascertain the resistance of 
elliptical tubes of wrought iron to collapse, compared with 
that of cylindrical tubes, when subjected to an external 
pressure. 

TABLE XLVI. 



Number of the ex- 
perimental tube. 


Size of tube. 


Pressure in lbs. 


Diameter in 
inches. 


Length in 
feet. 


Thickness in 

decimals of 

an inch. 


per square inch at 

which the tube 

collapsed. 


34 
35 


14 x 10^ 

20|XI5| 


5 

5^ 


•043 
•25 


6-5 
127-5 



The tube No. 34 was of the same thickness, and had the 
same quantity of material in its section, as the cylindrical 
tube No. 19 in Table XLIV. ; the latter collapsed with a 
pressure of 12-5 lbs. per square inch, and the former with a 
pressure of 6*5 lbs. per square inch, thus showing that a loss of 
strength equivalent to a pressure of 6 lbs. per square inch, or 
48 per cent., was caused by flattening the tube, so that its least 
diameter was reduced if inch, although the quantity of 
material in both tubes was exactly the same. 

The tube No. 35 was of the same thickness as No. 22 in 
Table XLIV., and had only fths of a square inch less 
material in its section, but it collapsed with a pressure of 
127-5 lbs. per square inch or 272-5 lbs. less than the cylin- 
drical tube, showing a loss of strength of 64-8, or nearly 65 
per cent., by flattening the tube until its least diameter was 
^th less than that of the true cylinder. 



270 On the Strength of Structures. 

Tubes exposed to Internal Pressure. 

A few experiments were carried out at the same time to 
ascertain whether the length of tubes similar to some of 
those previously enumerated, affected their resistance to an 
internal pressure. The results were, however, far from satis- 
factory, only two of the five tubes experimented upon being 
sound at the joint. These two were 6 inches diameter and 
12 inches and 48 inches long, respectively; the former burst 
with a pressure of 475 lbs., and the latter with 375 lbs. per 
square inch, apparently showing that the resistance varied in 
some degree with the length; but when practically considered, 
the result would appear to show that the length of the tube 
does not affect its strength under such circumstances, and 
both tubes would have burst with about the same pressure, 
had not the shorter one, owing to its extreme shortness and 
the consequent proximity of the point of fracture to the end 
supports, derived a great amount of its resistance from the 
fixing of the ends. 

Some further experiments were then carried out with 
leaden tubes of 3 inches diameter, and 14J inches and 31 
inches in' length, respectively. These tubes were of the same 
thickness of metal and burst with a pressure of 374 and 364 
lbs. per square inch respectively, from which it may be 
inferred that the shortness of a tube does not contribute to 
its resistance to an internal pressure, unless it is extremely 
short, say less than two or three times its diameter in length, 
when its apparent strength would be partly due to the 
support given by the ends of the tube. 

In the Perkins system of steam boilers, the boiler is 
composed of small tubes, which sustain with safety a pressure 
of 5,000 lbs. per square inch. To obtain greater economy, 
steam pressure increases from year to year; it is therefore 
probable that the steam boilers of the future will be 
gradually modified, by the more general employment of 
small tubes. 



Strength ofR ivctcd Strnctu res — Steam Bo Hers, &e. 271 



CHAPTER XVII. 

ON STRUCTURES SUBJECT TO INTERNAL PRESSURE. 

The present chapter will treat of the strength of cast-iron 
pipes and water tanks, and also of the relative advantages 
of hooped and solid cylindrical structures exposed to in- 
ternal pressure, as, for instance, in the case of guns and 
hydraulic press cylinders. 

Cast-iron Pipes. 

Cast-iron pipes are now so extensively used for various 
purposes, that it is of importance for the student to examine 
their power of resistance. 

In the majority of purposes for which cast-iron pipes are 
employed, as for the conveyance of gas or of water for the 
supply of towns, or for steam pipes or steam cylinders, or 
even for high-pressure hydraulic pipes, the question of 
strength is not so important as might be inferred from the 
trouble experienced in keeping them sound and water-tight. 
They are usually cast of such a thickness that their strength 
is apparently in excess of that required to resist the pressure 
acting on them. This superabundance of strength is given, 
because other practical considerations step in, which, as a 
rule, render it absolutely necessary to make such articles 
considerably stronger than is actually required for the work 
which they have to do. The practical considerations here 
referred to are the limits to thinness and soundness attain- 
able by the founder, and the comparatively fragile nature of 
cast-iron pipes, in bearing the rough handling to which they 
are subject in transit, and more especially the straining due 
to the subsidence of the earth from under them when laid 



272 



On the Strength of Structures. 



underground, or to its compression during the passage of 
heavy waggons over them. 

Reckoning the tenacity of cast iron of the quality which 
is frequently used for common pipes at 16,000 lbs. per 
square inch, it will be found by calculation, that very thin 
pipes of such iron would resist a great water pressure. Let 
us take a ring cut from a pipe, with a bore of 10 inches in 
diameter, and suppose the said ring to be 1 inch in length 
and J an inch in thickness, as in Fig. 63 ; this will give a 



ii 



Mililll, 



m- 



-- 10 ins. 
Fig. 63. 



=•[11 



substance of iron equal to one square inch of section to 
resist the water pressure. But one square inch will have an 
ultimate strength of 16,000 lbs., and may in such a case be 
safely strained to 4,000 lbs. To produce that stress, the 
pressure in the pipe must be 4,000 — 10, or 400 lbs., per 
square inch, or above 26 atmospheres, Hence, it will appear 
that, but .for the reasons already stated, gas and ordinary 
water pipes might be much thinner than they are usually 
made. 

In the Belgian Annexe of the Paris Exhibition of 1867, a 
cast-iron pipe was shown, 20 feet long and 28 inches in dia- 
meter, and varying from ith to fths of an inch in thickness. 
This pipe was proved with a pressure equal to 5 atmospheres. 
In this case the stress put upon the iron at the thinnest part 
of a ring, one inch in length, would be as follows : — The 
pressure of 5 atmospheres would be 75 lbs. per square inch, 
the number of inches being 28. The total substance of the 
two sides of the iron ring would be equal to ^ an inch. 
Then 75 x 28 will give 2,100 lbs. as the total pressure of 
the fluid which had to be resisted by the ^ inch of iron, or 
equal to a stress of 4,200 lbs. per square inch, thus only 



Structures stibject to Internal Pressure. 273 

straining the iron up to the quarter of its ultimate tenacity ; 
such a pipe, however, would be easily broken, unless great 
care was exercised in handling it. 

The water pressure pipes employed in connection with 
hydraulic crane works, are seldom used under a pressure 
of less than 700 lbs. per square inch, and the pressure varies 
from 46 to 68 atmospheres in different cases. The pipes 
conveying the water, when 3 inches in diameter, are made 
with fths of an inch of thickness, and are proved with 
2,500 lbs. internal pressure per square inch. Taking a 
ring of this pipe 1 inch in length, the water pressure tending 
to burst it will be 2,500 x 3 = 7,500 lbs., which has to be 
resisted by | x 2 = ij square inch of iron, which, for 
such a purpose, would be of rather a better quality than 
that for common pipes, probably having a tenacity of 
18,000 lbs. per square inch. This would give an ultimate 
resistance of 22,500 lbs., or three times the stress to which 
the ring is exposed, under proof, and the proof stress is 
fully three times greater than the stress during ordinary 
working. It might be inferred that such pipes were un- 
necessarily strong, but such is not the case ; owing to the 
numerous contingencies to which they are exposed, and 
to the effect of continued rusting while buried in the earth, 
they require an excess of strength, and experience fully con- 
firms the wisdom of allowing a large margin at the outset. 

Cast-iron Tanks. 

In the construction of round, square, or rectangular tanks, 
built up of cast-iron plates, which are united with wrought- 
iron bolts by means of flanges or ribs, which are cast upon 
the edge of the plate at right angles to it, different con- 
ditions exist to those met with in pipes which are of 
comparatively small diameter. Let us select a round 
water-tank as an example, which may be compared to an 
immense tube placed upon its end. The enlargement of the 
pipe into a water tank of say 100 feet in diameter by 25 feet 

T 



274 On the Strength of Structures. 

in depth, brings the question of strength into greater pro- 
minence. It is a very common error to suppose that the 
strength of the tank is not affected by the diameter, but, as 
we shall see, the diameter has a most important influence 
on the resisting powers of a tank. 

In the first place, a pressure or weight of 25 cubic feet of 
water, equal to 25,000 ounces, rests upon every square foot 
of surface of the bottom plates, but as these are here sup- 
posed to be lying upon a solid foundation, the strain on 
them may be disregarded. 

The pressure per square foot that comes upon the sides 
of the tank is only equal to the half of that which rests on 
the bottom, because at the surface the pressure is nil, while 
at the bottom it is, as before stated, equal to 25,000 ounces ; 
consequently the fluid pressure due to 12J feet, or 12,500 
ounces, is the average pressure that the side or circum- 
ference of the tank has to sustain, per square foot of surface. 

The above remarks apply to every kind of tank, but it 
would be a great waste of iron to make the upper tier of 
plates, in a tank, sufficiently thick to withstand the pressure 
of water at 12 J feet in depth, and it would be still worse 
to make the lower tier of plates only equal to the pressure 
of 12 \ feet, seeing that they have to withstand 25 feet. This 
renders it obvious that, in order to obtain the requisite 
strength with the minimum of iron, the bottom tier must be 
equal to the strain that comes upon them, and the thickness 
upwards must be gradually diminished to the top plates, 
which need only be of such a substance as will meet the 
various contingencies referred to, in connection with the 
casting and conveyance of pipes. 

If we select one foot of the lowest ring of iron, and 
assume the average pressure upon it to be 25 feet of water, 
and then consider it as similar to an inch ring of a pipe, 
we shall then see that the question of strength is important. 
The iron used for such a purpose would probably have a 
tenacity of 16,000 lbs. per square inch ; then we may inquire 



Structures subject to Internal Pressure. 275 

how much of such iron will be necessary to withstand the 
pressure, leaving out of consideration, for the present, any 
assistance which it derives from being fixed to the edge of 
the bottom of the tank. 

The tank is 100 feet in diameter, which, multiplied by 
25,000 ounces, the water pressure on every foot, is equal to 
a total pressure tending to burst the lower ring, equal to 
2,500,000 ounces. Suppose we resolve not to strain the iron 
above Jrd of its ultimate tenacity ; -Jrd of 16,000 lbs., when 
reduced to ounces for convenience, is equal to 85,333 — say 
85,000 ounces. Then, dividing the total water pressure on 
the ring, tending to tear it open, by 85,000, will give 
29*4 as the number of square inches of iron required (say 
30 inches) ; that is to say, the two sides of the ring should 
have between them 30 inches, and, each being 12 inches in 
length, the thickness would consequently have to be 1^ 
inch. If the tank is considered merely as a pipe, then 
1^ inch of thickness would be required, but if we take 
into account the assistance derived from its connection to 
the bottom plates, as well as the support due to the pro- 
jecting flanges, which act as ribs, then it will be seen that 
the \\ inch may be reduced to i-|- inch, with perfect 
safety. In the same way will have to be calculated the 
number and size of the wrought-iron bolts that are required 
to hold the plates together, and which ought to be at least 
equal in strength to the 30 inches of cast iron. 

In order still farther to reduce the substance of the plates 

and the cost of the tank, it is now customary not to rely 

entirely upon the cast iron, but to reduce the substance of 

the lowest plate still farther — say to 1 inch in thickness — 

and to make up the difference by wrought-iron bands or 

hoops, which are put on under tension, and which, by their 

greater tenacity and reliability, afford the necessary security. 

By such combinations, the practical engineer is in some 

measure enabled to attain the maximum of strength and 

minimum of cost 

t 2 



276 On the Strength of Structures. 

In the foregoing remarks on the strength of pipes which 
are comparatively thin, it has been assumed that, when they 
are exposed to internal pressure, the metal composing the 
pipe is all performing duty in its resistance, in the same 
manner as a bar of iron when pulled asunder by tensile force. 
This is not, strictly speaking, the case, although in large 
structures, such as the water-tank, it is very nearly accurate 
to assume the metal to be uniformly strained ; and, even in 
small water pipes, no error of. practical importance is in- 
troduced by that assumption. In thick pipes, or in cylinders 
for hydraulic presses, or in gun structures, it is, however, 
widely different; then it becomes imperative to treat the 
question in another manner. 

On the Strength of Hooped as compared with Solid 
Structures. 

It was pointed out by Professor Barlow, many years ago, 
that the strength of a pipe, hoop, or cylinder to resist in- 
ternal pressure is not in proportion to the mass or thickness 
of material of which it is composed, and that by adding to 
the thickness of a tube or a gun, or to the substance of the 
cylinder of a hydraulic press, or by increasing the thickness 
of an iron pipe, we do not thereby increase the strength, in 
proportion to the quantity of metal which is thus added. 
When a hollow cylindrical vessel is exposed to internal 
pressure (amounting in hydraulic presses to 3 tons per 
square inch of surface, and in guns to a still greater inten- 
sity) the pressure does not affect the whole mass of metal 
opposed to it in the same degree. The metal composing 
.the inner surface of the bore is first * affected, and as that 
part is extended, so the stress gradually reaches to the next 
lamina, but in a decreasing ratio, and this transmits it to 
the next, and so on, until at length the resistance of all are 
in some degree brought into active exercise. 

The important point to observe is, that the work which is 



Structures sicbject to Internal Pressure. 277 

performed by the successive concentric laminae, in resisting 
the internal pressure, is in exact proportion to the amount of 
stretching to which they are severally subjected. It is found 
by experiment that, when a ring is stretched by mechanical 
means, the outside does not expand so much as the interior ; 
this will appear to be self-evident, because if it did so, 
then the volume of the material composing the ring would 
actually be increased thereby, which is impossible ; but 
besides and independently of any experiment, as the outer 
circumference of the ring is necessarily longer than the inner 
surface, even if they did stretch an equal amount (if that 
were possible by a narrowing of the ring), the metal com- 
posing the two surfaces would not even then be strained 
equally, on account of the stretch on the outside being 
distributed over the circumference of a larger ring than 
that on the inside. And upon the above conclusion some 
most important practical deductions rest. 

In attempting to design a gun or cylinder, which shall be 
theoretically perfect, so that the whole of the molecules 
which compose the cylindrical part of the structure shall 
stretch alike, then the metal should be so disposed that, at 
the moment of pressure or explosion, every part thereof 
shall be equally ready to take its full share of the duty at 
once, and in proportion to its ability, and should be con- 
structed with the tension previously put on the alert, so as 
to be always in readiness, and without the outer portion 
having to wait for the stretching of the interior to give it 
employment. 

Up to the present time, no practical system of construct- 
ing either guns or hydraulic cylinders comes nearly up to 
these theoretical conditions ; the nearest approach is pro- 
bably attained by building up the cylinder with fine wire, 
which is wound round an interior barrel, the wire being 
put on under definite tension ; but such an arrangement, 
although fulfilling one set of conditions, would evidently be 
weak in the longitudinal direction of the gun, unless all the 



2 J 8 On the Strength of Structures. 

wires were soldered together into a homogeneous mass, and 
even then the result would be doubtful. 

Another approximation to the theoretical conditions is 
secured, in the American system of casting iron guns, by 
cooling the mass of hot metal from the interior of the bore, 
instead of by the usual method of allowing the mass to 
remain in the foundry mould, until the heat has passed away 
by conduction through the exterior. In the latter case, it 
may be inferred that the outside of the mass of metal is 
necessarily colder than the centre of the solid block, and 
consequently will have contracted more on that account, 
and so have become stretched upon the warmer and more 
expanded interior, until at length the whole of the heat has 
passed away, and the inside consequently has become 
equally cooled, which will then likewise have contracted 
and taken up its normal dimensions, and will thus find 
itself at a disadvantage on account of the previous stretch- 
ing and final setting of the outer portion. It will then 
necessarily become less dense, and, hence, to some extent, 
it will lose the full grip and support of the exterior metal 
composing the mass. 

By the American plan, on the other hand, the gun is cast 
hollow on a mandril, with what is termed a water-core — 
namely, a tube in which a constantly circulating -stream of 
water is kept up, to carry off the heat rapidly from the 
centre, thus entirely reversing the conditions, and so causing 
each lamina in succession to grip hard upon that which it 
encloses. 

In carrying out this cooling operation, shortly after casting, 
the stream of water is first directed through the core-barrel, 
entering by a pipe down the centre and then rising through 
the annular space between the pipe and the core-barrel, and 
escaping by passing away over the top of the dead head. 
In this process of cooling a heavy gun by a stream of water, 
the procedure may have to be continued for a couple of 
days, and when the gun has partly cooled^ the core-barrel 



Structures subject to Internal Pressure. 279 

is extracted, and the water is made to flow into the 
bore by a pipe, in a similar manner as before, but the 
water now escapes in contact with the actual bore of the 
gun; meanwhile a fire is kept up all round the exterior 
mould of the gun, in order to protract the high temperature 
of the outside, and prevent the heat from escaping in that 
direction. 

Independently of the foregoing consideration, the question 
of strength in a solid cast-iron cylinder or gun is likewise 
affected by the exterior form, the presence of the gun 
trunnions, or, indeed, of any other massive projections or 
irregularities of outline, and still more by the shape given 
to the breech. All these points determine strength or 
weakness, inasmuch as these forms or shapes create new 
conditions, which greatly affect the direction in which the 
waves of heat pass out, from the interior of the mass, 
to the nearest point of exit into space. It is found that all 
such irregularity introduces elements of discordance, into 
that which would otherwise be the harmonious and natural 
order of crystallisation, any departure from which is always 
accompanied by corresponding weakness. 

A good illustration of this kind of weakness was afforded 
by the accident which occurred in raising the Britannia 
Tubular Bridge. The hydraulic cylinders were originally 
made with a flat bottom, like that of a drin king-glass 
(as shown in Fig. 64) ; the cylindrical part of the casting 
had the crystals radial from the inside, but in the bottom 
part the crystals were perpendicular to the flat end, and 
at the points where the two different arrangements of 
crystals come together, at an angle — namely, at a line 
drawn from the inner to the outer corners — there were 
the lines of weakness. Hence it was that, although con- 
siderably thicker, the cylinder failed at those points. 

The second or substitute cylinder was made with a hemi- 
spherical end (as in Fig. 65), and in it the radiating crystals 
were all arranged in lines more nearly parallel, although of 



28o 



On the Strength of Structures. 



course not truly so. As thus made, it was found to be 
amply sufficient in strength, even with the same amount of 
metal in the mass. The foregoing accident was the means 
of drawing public attention to the subject. Many engineers 
found it to agree with their former experience, and many 





Fig. 64. 



Fig. 65. 



had previously been modifying the forms of structures with- 
out knowing the natural law. 

The subject is well illustrated by a singular phenomenon 
that is observed in chilled shells, in which, from the effect 
of the sudden deprivation of heat, the lines of crystallisa- 
tion are very clearly marked, and, when broken, the order 
of crystallisation is exhibited most convincingly. In such 
shells there occurs an apparent inconsistency with this reading 
of the law, namely, at the point of the shell, where in 
every case the crystals take a curved direction rather than 



Structures stibject to Internal Pressure. 281 



Thi 



S 13 



straight out into space (as shown at Fig. 66). 
due to the following cause : — The 
shell is cast on end, with the point 
downwards. When the liquid metal 
is poured into the mould, it is, as 
a matter of course, in contact all 
over; and during the period that 
it remains a liquid, it naturally fol- 
lows the gradually expanding mould 
or vessel in which it is contained ; 
but as it begins, from the effect of 
the chill, to form an exterior crust, 
the time arrives when the body of the 
casting is not in actual contact with 
the mould, and consequently the 
rate of conduction of heat is thereby 
lessened, but not so with the point 
of the shell, which is kept at the 
bottom of the mould by the effect 
due to the gravity of the mass. 
Hence, the point of contact becomes 
a new line of direction, competing with the sides of the 
mould, and the effect of the two determines the curved form 
of the crystals, as shown in every instance. 

In past times, it was assumed that cast iron must ne- 
cessarily be homogeneous, instead of which it is otherwise, 
any sudden divergence of the escaping lines of heat causing 
a change in the direction of the crystalline formation, and 
rendering that part weaker than the general mass ; and as 
with a chain so in a gun or cylinder, the strength is only 
equal to that of the weakest point. The knowledge and 
right application of this lav/ will in time affect the form of 
many structures, and lead to the use of cast iron for pur- 
poses where wrought iron is now employed. 

Already most of our engineers are constructing their 
hydraulic cylinders on the plan shown in Fig. 65, and 




282 On the Strength of Structures. 

the Americans are constructing their cast-iron guns in form 
not unlike a soda-water bottle, which is nearly in strict ac- 
cordance with this law of crystallisation, the exterior surface 
being arranged so as to invite the heat outwards in a nearly 
uniform current in all directions. 



Built-up Guns. 

We have already indicated that strength is derived from 
putting the interior mass of a cast-iron gun or cylinder 
under compression, by the initial tension of the metal 
nearer to the outside, due to cooling from the interior, 
and thus approximating to the condition of the gun made 
with fine wire. But it has further to be observed that the 
same conditions would be obtained if the structure were 
composed of a great number of thin hoops, put on one 
over the other, but under the same tension as the wire, if 
this were practicable, which it is not commercially, on 
account of the expense in producing such accuracy as 
would ensure the specified tension. But although it may 
not be convenient to construct such articles with a great 
number of thin hoops, still, by a slight departure from the 
theoretical conditions, namely, by using a smaller number of 
thick hoops, an approach may be made to great strength, and 
by thoroughly practicable means. In this way we can fabricate 
large guns or cylinders, by taking the several parts in detail, 
and combining them into a comparatively perfect whole, 
at a moderate expense, and with such an approximation to 
the theoretical conditions as affords great satisfaction ; the 
great condition aimed at being to equalise the stress 
throughout the mass, when under tension from internal 
pressure, and this is the principle of the system now pursued 
both at Woolwich and Elswick in the construction of what 
are termed ' built-up guns.' 

The wrought-iron hoops are made of any diameter or 
length, by first making a bar of the required section, and cf 



Structures subject to Internal Pressure. 283 

sufficient length to contain the necessary quantity of iron ; 
this long bar is then heated in a furnace, and by mechanical 
means it is wound round a mandril into the condition of a 
coiled bar. This coil is removed from the mandril and then 
put into a furnace, made welding hot, and then put under 
a steam hammer, and the loose coil is then welded into a 
close cylinder or hoop of wrought iron. Or, the above 
process may be varied, in the formation of exceptionally 
thick hoops, by the winding of one coil over another, before 
the welding operation is performed. When the hoop is 
forged, it is put into the lathe or other machine, for boring 
and turning it to the required dimensions. 

On the first consideration of this subject, the mind is 
rather unwilling to believe that in such articles as are here 
referred to, when composed of fine wire or a number of thin 
rings or hoops, or even of a smaller number of thick 
hoops, as used in the construction of modern built-up 
guns or cylinders, that such a mode of construction can 
have the same solidity and strength to resist internal 
pressure, as a similarly formed homogeneous mass in one 
forging or casting; still more so, when that mass is made 
of the best . material, and in practice shows great en- 
durance, as is the case with the fine cast-steel guns made 
by M. Krupp of Essen. Besides, it might further appear 
that in the built-up structure, when consisting of a hooped 
fabric, in which the mass composing it is discordant, being 
neither homogeneous nor working in harmony — that each 
hoop is under different conditions, that the barrel and 
the inner hoops are existing under compression, while 
the exterior hoops are under great tension. Nevertheless, 
the positive results show that no sensible practical dis- 
advantage is found to arise from the want of homogeneity, 
while the homogeneous or solid guns are not more reliable, 
if indeed they are equally reliable. By the building-up 
system, we are enabled to have the finest steel for the 
interior barrel, and a cheaper material, wrought iron, for 



284 On the Strength of Structures, 

the remainder ; and although wrought iron is a cheaper and, 
in one sense, an inferior material, yet for this special purpose, 
from its great toughness, it may, as a general rule, be con- 
sidered fully equal, if not superior, to steel of greater ulti- 
mate tenacity. 

From these remarks, it will be seen that the subject admits 
of a difference of opinion, and such a difference does exist 
amongst those well qualified to judge, and who have given 
the subject great attention ; but still the fact remains that 
the strain which comes upon the interior of a gun first acts 
on the inside of the bore, and as that part of the metal be- 
comes stretched, so the stress gradually reaches the outside 
in a diminishing degree, and hence the outer metal cannot 
contribute its full share of duty, unless it has an initial 
tension. 

This principle of initial tension is employed, in the 
modern manufacturing system of building up wrought-iron 
and steel guns and hydraulic cylinders, by the various modes 
of either shrinking or pressing one hoop, under tension, over 
another hoop. 

The shrinking system, which was introduced by Sir William 
Armstrong, for the construction of artillery, has been exten- 
sively applied, and at the present time it appears likely to 
supersede all other systems, from the circumstance that, by 
this simple arrangement, the best practical results as to 
quality and cost have been obtained. 

After taking all things into consideration, greater practical- 
advantages have probably been attained by this system than 
by any other, and as the same principle of construction is 
equally applicable to hydraulic cylinders, the student should 
endeavour to understand its general bearing. 

To take the gun as an example, the principal part is 
the bore, formed within the inner barrel, which constitutes 
the foundation or core upon which the exterior hoop struc- 
ture is to be built up. The chief object of the hoops is to 
render all the support of which they are severally capable, 



Structures subject to Internal Pressure. 285 

by the principle of having the portion of work that they can 
do, partly put upon them in the original making of the gun. 
The inner barrel is, then, the most important part ; it is 
made of cast steel of a mild quality, and carefully tempered 
in oil, so as to bring out its strength and elasticity. It is 
then covered with a thick hoop, or a series of thick hoops in 
succession, the one over the other, and each under regu- 
lated tension, as determined by calculation of the relative 
dimensions of the parts that have to grip and the part which 
has to be gripped, and they are so combined into a whole 
that each hoop shall take its full duty at the critical moment, 
and that the total tension put upon the several hoops shall 
be at least equal to or exceed the effect of the explosion. 

The possibility of attaining such conditions is due to the 
knowledge of the fact that iron stretches about the 10 ^ 00 th 
part of an inch, per inch of length, by a ton of stress. It 
therefore becomes a simple matter of calculation, to deter- 
mine the difference of dimensions between the outside of 
the inner surface and the interior of the outer that will give 
the required tension, and consequently the stretch and 
specified grip in tons of positive support. 

When the two surfaces are made to the required diameters, 
then the outer hoop is heated to redness, which causes it to 
expand about -rjjo-th part of its linear dimensions ; it is then 
carefully slipped over the inner part, upon which it gradually 
cools and contracts, with the force, in tons per square inch, 
upon the metal, intended to be applied. 

As the greatest stress or pressure from the explosion will 
be brought to bear, first, upon the interior of the inner barrel, 
and from that will be passed on to the hoops, the object is 
to concentrate the grip of all the hoops upon the inner 
barrel. The effect of the united grip of a series of hoops, 
due to shrinking one hoop over another, is, that the grip of 
an outer hoop serves partly to undo a portion of the grip of 
the hoop or hoops which are under it, thus putting the 
entire structure into a state of lively activity; and the 



286 0?i the Strength of Structures. 

several hoops are always standing at attention, to perform 
the required duty ; but in determining the precise dimen- 
sions which will assign the proper tension and duty to each 
hoop, all the alteration or disturbance of dimension, and' 
consequently of tension, thus caused by the successive grip. 
of hoop over hoop must be taken into account, in esta- 
blishing the difference of dimension between the inner 
surface of the gripping hoop and the outer surface of the 
under hoops, as also the relative grip to be put upon 
the hoop next to the barrel, and the intermediate and outer 
hoop. 

In the attempt, so far as it may be practicable, to place 
the whole structure in such a condition of lively tension as 
that, at the moment of explosion, each hoop in succession 
will be already under the assigned load, and all of them take 
the same duty in tons per square inch, it is necessary that 
the amount of tension put upon the several hoops should 
not be equal, but should be inversely as the stress that 
would reach them severally, if the structure were a solid 
mass of metal. 

Until recently it was generally considered, on theoretical 
grounds, that the force or resistance exerted by the dif- 
ferent parts of a solid cylinder, was inversely as the square 
of the distance of the parts from the centre, • but recent 
experiments, made by stretching rings within rings, would 
seem to prove that the stress is nearer to the inverse ratio, 
or at least nearer to that than to the former. The cause 
for any such uncertainty is owing to the physical nature of 
materials, and arises from a complication of various reasons 
due to the properties of the metal — its elasticity, ductility, 
and compressibility, which all step in to interfere, com- 
plicate, and introduce uncertainty, and all come into active 
play and thereby affect the apparent result. But all experi- 
ments point in the one direction — namely, that the strain 
comes upon the interior in all its force, and gradually 
decreases inversely as the distance from the centre, or 



Structures subject to Internal Pressure. 287 

nearly so. Therefore when a gun is completed, the tension 
of the structure should be greatest at the outside, and 
gradually decreasing to the inner barrel, which should be 
under compression, so that at the moment of greatest stress 
no part should be strained beyond the apparent limit of 
elasticity. 

To those who are not familiar with the practical working 
out of this system of building up concentric structures, it 
might appear that some difficulty would be experienced, in 
obtaining such accuracy as would ensure the required degree 
of tension, with uniformity ; but such is not the case, from 
the circumstance that the system of manufacturing has been 
so organised as to reduce the results of measurement to a 
certainty. The hoop is first bored to the intended dimension; 
it is then carefully measured by instruments, that by the aid 
of the vernier or micrometer read off the dimensions to 
the To-g-o o tn P art °f an mcn - As tne interior surface may 
not be perfectly parallel, the correct size is noted at dif- 
ferent points and written down on paper. To these dimen- 
sions are added the amount of difference required (namely, 
Towotli of an inch, per inch, for each ton of tension or 
grip). The total dimension gives the size of the part on 
which it has to be shrunk. These new dimensions are 
recorded, and with the corresponding measuring instru- 
ments duly marked in ink, and the. same dimension written 
upon a sketch • the paper and guages pass on to a turning- 
lathe, where the respective parts of the structure are reduced 
to the required diameter, an operation necessarily requiring 
skill and care on the part of the workman, but no difficulty 
is experienced. 

Should the operation be performed erroneously, by making 
the grip too small, then it is only necessary to reserve the 
hoop for the next gun, and select a smaller hoop for the 
one in hand, these differences being only a few thousandths 
of an inch. If, on the other hand, too much metal has 
been left on the exterior diameter, thus creating a greater 



288 On the Strength of Structures. 

tension upon the metal composing the hoop than was 
intended, the error will be detected by the system of 
check, when it reaches the official viewer at the next 
stage, and is then either passed or returned by him for 
correction by the turner. 

From some observations which were made on the above 
point at the early stage of the manufacture, before much 
experience had been gained in regard to the shrinking of 
exterior hoops, it seemed more than probable, from certain 
results, that the strength of the hoop was not much, if at 
all, imperilled by too much tension being put upon it ; that 
the iron hoop, from being hot, probably allowed itself to 
be stretched or permanently wire-drawn to a certain extent 
without injury, and thereby was enabled to accommodate 
itself to a wrong diameter. With a hoop under different con- 
ditions, as regards temperature, the result would be disad- 
vantageous, and might end in fracture, owing to the want 
of sufficient ductility in cold iron. 

Longitudinal Strain. 

In considering the strength of guns, and the causes which 
determine their failure, it has to be clearly understood that 
besides the force tending to burst them in the lateral 
direction — that is to say, outwards circumferentially — they 
are also subjected to another force which tends to destroy 
them in the direction of their length ; the same force, which 
sends the shot forward, has an equal reaction on the breech 
of the gun, thus tending to separate it from the barrel. 

The student, on considering these two distinct strains 
or forces, will be led to perceive that the breech of a gun 
is in some respects like a beam or girder ; it must have a 
neutral surface ; there must be some point where these two 
forces are not favourably situated for harmonious action. 

If we suppose the gun to be composed of some substance 
resembling highly elastic india-rubber, it will be readily 



Structures subject to Internal Pressure. 289 

conceived that, under such imaginary circumstances, at the 
moment of explosion, the whole of the rear part of the gun 
would be extended in every direction, like a bladder, or as 
we see in the operation of glass-blowing. It is quite 
different, however, in the case of an iron or steel structure ; 
there is not the same freedom for distension in every 
direction ; and hence, when the metal is overcome, the 
usual result of the explosion is the blowing out of the breech, 
away from the barrel, and the bursting of the cylindrical 
part next to the breech, generally leaving the fore part of the 
gun entire. 

The longitudinal strain, then, which comes upon the 
breech, is derived from the same force as that which sends 
the shot forward, but with this difference, however, that the 
gun not being so light as the shot, it recoils a propor- 
tionately less distance. The safety of a gun will depend 
upon the mass of solid metal composing the breech, even 
when the metal is merely considered to resemble an 
ordinary steam-hammer anvil-block, which is the instrument 
for receiving the force of the blow of the falling hammer ; 
and every observing forgeman knows how efficient is the 
blow with a heavy anvil-block, and how well it stands up 
to its work, as compared with a light one. Upon the same 
principle, the heavier or more massive the breech of the 
gun, so the less is the tendency for it to recoil and break 
away from the cylindrical portion, by the effect due to the 
blow of the explosion. 

For the foregoing reasons, all designers of guns who 
know their work introduce as much solid metal as possible, 
or as much as may be admissible, into the breech of a gun, 
merely to act the part of an anvil-block, and thus prevent 
the neutral surface, where the two forces unite, from being 
unnecessarily disturbed, or to such an extent as would 
endanger the safety of the gun structure. 

u 



290 On the Strength of Structzires. 



Strengthening of Cast-Iron Guns. 

The gradual dawning of the foregoing principles, on the 
minds of many individuals, has led to several attempts at 
strengthening ordinary cast-iron guns, either by exterior 
hooping with wrought iron, or by lining the interior, either 
with wrought iron or with oil-tempered steel. The former 
system has hitherto been unsuccessful, no doubt owing to 
the weak interior of cast iron giving way, before the assist- 
ance of the hoops came into exercise, and such guns have 
seldom done more work with the hoops, than might have 
been expected without their presence ; hence, for the present, 
that system has been abandoned. 

Cast-iron guns, when strengthened on the latter system 
— namely, by the introduction of an inner lining of some 
stronger material — have afforded most satisfactory results, 
and many guns have, therefore, been treated on this prin- 
ciple. Various plans have been proposed, both by Major 
Palliser and Mr. Parsons, but these do not differ much in 
regard to their general principle ; the chief peculiarities of 
the different plans are in the details, which may here be 
disregarded. 

The general principle upon which all such guns are 
strengthened is founded on the natural law, discovered by 
Barlow, and by him demonstrated mathematically, and 
which is generally assented to by all who have followed 
in his footsteps, and which has already been referred to in 
connection with the subject of built-up structures of wrought 
iron. 

On the assumption, therefore, that when a cast-iron gun 
is exposed to internal pressure, the metal composing it is 
thereby strained unequally, if the solid gun cylinder were 
supposed to be divided into a number of thin concentric 
cylinders, the extension of each under strain would be, ac- 
cording to Barlow, inversely as the square of the diameter; 



Structures subject to Internal Pressure. 29 1 

and as the strain is in exact proportion to the extension, 
then the strain will vary in the same ratio. 

The interior of the gun is therefore subjected to the 
greatest strain, and the exterior to the least strain ; conse- 
quently the interior has to stretch more than the outside. 
If, then, the interior is made of a stronger material and a 
more extensible metal than the exterior, by inserting into 
the cast-iron gun a tube of wrought iron or steel, the metals so 
arranged will be placed in accordance with the true theoretical 
conditions, and each portion will take its appropriate share 
of the work. When a discharge of the gun takes place, the 
inner wrought-iron or tempered steel tube will offer the first 
resistance and take a large portion of the strain; but, in 
doing so, it will stretch three times as much as it would 
have done had it been made of cast iron, and yet without 
exceeding its apparent elastic limit. But its exterior sur- 
face will necessarily stretch less than its interior, and there- 
fore the cast iron into which it is fitted will only be stretched 
to the same extent, a point of importance. If the steel tube 
is properly fitted into the cast-iron bore, the fit being what 
may be termed easy, or so proportioned as to give such an 
amount of extension to the steel tube as will be just suffi- 
cient to stretch the cast iron up to a point a little under its 
elastic limit, at the moment of explosion, then the cast iron 
will not be injured. But these conditions imply a degree of 
nicety which may seem difficult to attain, by those who 
are not initiated, but which in reality is easily accomplished, 
practically, by the aid of the vernier. 

A remarkable feature in connection with this part of the 
subject, and which the student should note, is the para- 
doxical fact, which can be satisfactorily proved, that by 
boring out a cast-iron gun to receive a steel tube, even 
to the extent of half its thickness — that is to say, by 
cutting away half its substance — the gun is thereby rendered 
stronger than it was before — not much stronger, but still the 
difference is for the better. This, however, will only hold 



292 On the Strength of Structures. 

good when the internal strain is applied on the same dia- 
meter of bore as it was originally. This is simply due to a 
greater harmony existing among the laminae, because when 
the difference between the diameter of the enlarged bore 
and the external diameter is smaller than it was before, 
there is now less difference in the relative extensions, and 
consequently the various laminae act together more uni- 
formly, and therefore more advantageously. 

Likewise the longitudinal strength of the gun is not in- 
jured, for the areas of circles being as their diameters 
squared, half the thickness of the gun may be bored out, 
and it will still retain more than half of its longitudinal 
strength ; and as the longitudinal strain on a gun is only 
about one-fourth of the tangential strain, the gun will still 
possess an ample excess of longitudinal strength. These 
considerations have, therefore, led to the system of strength- 
ening cast-iron guns by the insertion of a steel or wrought- 
iron lining, which has given high results, although not 
equal to those obtained with built-up guns of steel and 
wrought iron. 

The student should not overlook the foregoing principles, 
because his pursuits may lie in some other direction. The 
same principles apply in numerous cases, wherever hollow 
cylinders of cast iron or other metal are exposed to internal 
pressure, of sufficient force to call their full strength into 
requisition. 

If the study of this unpretending little volume has pro- 
duced the desired effect on the mind of the earnest student, 
he will, doubtless, have perceived how much his daily 
routine duty in the workshop is associated with natural 
science and practical art, and how very little even of art 
belongs entirely to man or to man's doings ; that all the 
materials to which reference has been made, together with 
all their properties, exist irrespective of man ; and that the 
principles which determine strength in structures of any 
kind— beams, gearing, pillars, cranes, boilers, and even guns 



Structures subject to Internal Pressure. 293 

— are all natural principles which have simply to be complied 
with or taken advantage of, in order to make the best of 
things as they are found in the world. There is a sort of 
conventional notion, especially in the workshop, that to 
men belongs the credit of inventing principles ; those in- 
volved in the forms given to beams, for example, in order 
to obtain the greatest strength with a given quantity of 
material. But it is otherwise; men have only gradually 
perceived the natural principles on which strength depends, 
nd then endeavoured approximately to comply with their 
requirements. Generally, natural principles can only be 
approximately complied with, because numerous practical 
difficulties present themselves in consequence of our im- 
perfect knowledge, and bar the way to the true form in 
carrying out practical work. So it is in everything ; the 
natural law, for example, upon which the mechanical device 
called a lever is founded, is the same principle which 
governs all the other so-called mechanical powers, however 
variously devised, and explains all our mechanical ex- 
pedients for the conversion of force or motion. By no 
agency can mechanical work be lost or gained, however 
ingenious the contrivance ; it can only be wasted or mis- 
applied for the intended object, by the unnecessary friction 
or by the imperfect arrangements of man in accomplishing 
his purpose. The law itself is perfectly simple, and when 
the full knowledge of the law is possessed by all workmen 
engaged in its application, in the wide domain of applied 
mechanics, we are fully warranted in the anticipation that 
our apparatus will be gradually simplified, that the various 
members of complicated structures will be so proportioned 
to the stress which comes upon them, that a greater uni- 
formity of strength and saving of material will thereby be 
achieved. So it is likewise with the most common opera- 
tions of the workshop ; all of them depend on some natural 
principle ; the tempering of a chisel, the angle of a cutting 
tool, the shape given to a hammer, so as to give the required 



294 On the Strength of Structures. 

quality of blow, the speed suitable for the cutting of dif- 
ferent materials, and every other kind of operation or 
process, all are founded upon unalterable laws of nature : 
our province is merely to apply materials, wherewith to direct 
and control the natural laws, in order to effect some de- 
finite end of our own. 

From day to day, men are seeing new ways of turning 
these natural principles to account ; it has been the same 
for thousands of years ; these new applications are some- 
times called discoveries or inventions, but all these new 
contrivances of the present, existed at the beginning of 
applied mechanics, only with this difference, that men did 
not perceive them. So it is now ; we are groping in the 
dark for new appliances, but all the appliances of the future 
are already existing in nature, but our ignorance prevents 
us from seeing them at the present time ; and every fresh 
ray of light, that shows us how to apply natural law and 
natural material in a new way, will never bring us nearer to 
the end : every improvement will only form a clue to other 
applications, so that invention will never cease, nor will 
men's work be done ; — the gradual result will be to enable us 
to live with less expenditure of material and labour, and 
thus to ameliorate the condition of the whole human family. 

It is scarcely one hundred years ago since it was considered 
next to impossible to turn or bore cast iron ; now we can 
perceive how thin the veil was which obscured that pos- 
sibility — that it was only necessary to move the surface at 
a certain velocity. At that period it was thought essential 
to take the power from the motor at a slow velocity, thus 
entailing heavy cumbrous mechanism- to transmit the power ; 
yet men knew the law then just as well as we do now, 
but they did not realise it with our vividness, so as to 
warrant them in changing their system ; quickening the 
motion would at once have reduced the cost both of the 
power required and the materials employed. 

It is not many years since it was deemed impracticable 



Structures subject to Internal Pressure. 295 

to sharpen hard steel circular cutters, without first softening 
them, yet we now see that it can be done, as easily as 
sharpening a drill at the grindstone, and by an arrangement 
as old as the cutting of diamonds, and upon the same 
principle. The effect due to velocity has yet to play an 
important part in many of our modes of treating materials ; 
the old experiment of firing a candle through a door, or of 
firing a pistol bullet through a pane of glass, without crack- 
ing the pane, exhibited an important principle, but the last 
generation could not read the lesson ; by understanding 
this principle and applying it in other directions, refractory 
granite or other hard substances can be treated with ease 
and facility. 

Again, take the steam-engine, for example. The little 
steam-engine which worked in the courtyard of Hero of 
Alexandria, two thousand years ago, was no doubt con- 
sidered wonderful in its time ; but if the indicator diagrams 
of its performance, together with the quantity of fuel con- 
sumed, per horse-power per hour, had been handed down 
to us, we, with our more advanced experience, would not 
be surprised to find the consumption of coal equal to 100 
lbs. — or, going back only two hundred years, it is probable 
that Captain Savery's engines consumed 50 lbs. — per horse- 
power per hour. 

Then James Watt, by fresh devices, took advantage 
of nature's secret working in better ways, and thus re- 
duced the consumption to 10 lbs. of coal, and, by the 
further development of the same principles, the consump- 
tion of some modern engines is within a fraction of 2 
lbs. of coal, per horse-power per hour. But are we to re- 
main at 2 lbs. ? We learn from Joule's equivalent that 
the heat which is required to raise a pound of water i° 
would raise 772 lbs. 1 foot, if entirely converted into me- 
chanical work ; if so, and there is no reason to doubt, 
then our work with coal and steam is scarcely begun ; our 
best engines do not perform one-tenth of that duty. Those 



296 On the Strength of Structures, 

who are now engaged in the contest are prone to think, 
that with 2 lbs. of coal, per horse-power per hour, we are 
near the limit of improvement, but let not the student think 
so ; we have every reason to believe that unlimited devices 
are stowed away in the archives of nature, which, one by 
one, will in due time be found by the earnest seeker, 
and will open up avenues of economy that are unknown 
in our present philosophy. The thin curtain which hides 
from us the means of obtaining a horse-power, with 1 lb. 
of coal per hour, is gradually being withdrawn, and the way 
of overcoming certain practical difficulties, that bar the way 
at the present time, is clearing up from year to year. 

When the majority of men, who are engaged in the 
fabrication of materials into definite forms, in order to 
prepare them severally for some mechanical combination, for 
the conversion of force or motion, are all well imbued with 
the knowledge of natural principles, the effect must be 
great. There are now many thinking minds directed to 
the study of such questions, by the teaching of art and 
science, whose influence will soon make itself felt in every 
direction, and through all our operations. 

The object of these concluding remarks is to draw the 
attention of the student more to the physical and experi- 
mental basis of the study of applied mechanics, force, 
motion, structures, and material than is usually given. 
The cultivation of the habit of looking for the natural 
laws which underlie all mechanical operations will prepare 
the mind for the higher and, at present, unknown practical 
questions that are laid up in the future. 



INDEX. 



ALU 

ALUMINIUM 
BRONZE, 97 
Ash timber, 108 



BABBITT'S METAL, 
98 
Beams and girders, 157-159 

— cylindrical, stiffness of, 

181 

— strength of, 170 

— flexible, made rigid, 8 

— of uniform strength, 172 

— rectangular, deflection 

of, 180 

solid, 169 

stiffness of, 181 

strongest form of, 170 

— rigid, 8 

— secure fixing at ends of, 

160 

— square, strength of, 170 
stiffness of, 181 

— trussed, counterbraces, 

210 

diagram of, 209 

movable load on, 209 

— — stress of, 209 
Beech timber. 109 
Bell-metal, 98 

— preservation of, 98 
Boilers, arrangement of 

plates in, 241 

— copper for, 79 

— strength of, 253, 256 

— testing of, 251 

— tubes, small, 270 

— tubular, 257, 258 

fire-box, 260 

smoke-box, 261 

stays, 260 

strength of, 258 

— weakened by improper 

arrangement, 257 

— wear through restless- 

ness of, 257 
Brass, 87 

— composition of, 88 

— effect of lead in, 88 

— fusibility of, 88 



CAS 

Brass — cont. 

— specific gravity of, 88 

— tenacity of, 89 
Bridles, testing, 17 
Bronze aluminium, 97 

— casting of, 97 

— composition of, 97 

— cost of, 97 

— experiments with, 97 

— and gun-metal, 82 

— compression of, 87 

— experiments with, at 

Woolwich, 86 

— exposure of, in furnace, 

84 

— furnace, treatment of, 86 

— fusibility of, 84 

— Muschenbroeck's ex- 

periments with, 85 

— Rennie's experiments 

with, 85 

— smelting, 84 _ 

— specific gravity of, 83 

— Wade's experiments 

with, 83, 86 
Butt joints, 267 



CANTILEVERS, 
FLANGED, 173 
Carbon' in cast iron, 31 
wrought iron, per- 
centage of, 48 
Cast-iron, 30 

— carbon in, 31 

— closeness of structure, 35 

— columns, 200 

with flat ends, 201 

rounded ends, 201 

— compared with wrought 

iron, 39, 54 

— compression of, 40 

— crude metal, 30 

— depending on tempera- 

ture, 44 

— effect of repeated de- 

flection, 128 

— elasticity of, 38 

— experiments with, 38, 39 

— fluxes of, 30 



COL 

Cast-iron — cont. 

— fluidity of, 35 

— for castings, 35 

— girders, 35, 167 

— guns, 32 

— in dry mould, 35 
testing machine, 32 

— limit of stress of, 33 

— liquid, 31 

— mixing of, 32, 36 

— Nova Scotia, 38 

— obscure points of, 30 

— ore refractory, 30 

— permanent elongation 

of, 37 
set of, 33, 38, 39 

— proportion of carbon in, 

32 

— remelting of, 44 

— rigidity of, 35 

— rough testing of, 35 

— specific gravity of, 27 

— specimens, short, crush- 

ing of, 44 

— strength of, 32, 34, 45 

— tensile strength of, 33 

— test bars, 36 
beam, 37 

— testing by hydraulic 

press, 36 
10-feet bars, 37 

— tests of, 36 

■ — under impact, 45 
Chains, proof strains of, 153 

— sorts of, 153 

— strength of, rules for, 154 

— wrought-iron, 52 
Collapse, 250 

— experiments by Fair- 

bairn, 263 

— — with butt joints, 672 

— experiments with over- 

lap do., 267 

— of circular tubes, 267 
elliptical tubes, 269 

— resistance to, 262 
Columns, 198 

— cast-iron, 200 

with flat ends, 201 

rounded ends, 201 



298 



Index. 



COL 

Columns — cont. 

— crushing of, 198 

— cylindrical, wrought- 

iron, 203 

— deflection of, 198 

— flexure of, 198 

— long, strength of, 195 

— parabolic, 199 

— practical deductions for, 

— rectangular, wrought- 

iron, 202 

— rigidity of, 199 

— short, strength of, 195 

— strength as depending 

on fixing, 196, 197 

— taper, 199 

— wrought-iron, 202 

cylindrical, 203 

strength of, 204 

Compression of cast iron, 40 

— of wrought iron, 40 
Constants, examples of, 

174, 175 

— of strength and deflec- 

tion, 176 

— use of, 173 
Contraction and expansion 

in boilers, 250 
Copper, 77 

— affected by temperature, 

79 

— alloys of, 77 

— and tin, 83 

— annealing of, 78 

— effective working of, 79 

— forging of, 78 

— for steam boilers, 79 

— in castings, 79 
■ — purity of, 77 

— refining of, 78 

— rigidity of, 78 

— specific gravity of, 79 

— strength of, 77 

— tenacity of, uncertain, 77 

— with phosphorus, 81 
Corrugated ring, 251 
Crane, hydraulic (see hy- 
draulic crane) 

— steam (see steam crane) 

— overhead travelling, 209 
Crank shaft, 140 

Crude metal, cast iron, 30 
Crushing cast iron, short 

specimens of, 44 
Cutting instruments, 

strength of, 194 
Cylinders, hydraulic, 279 
Cylindrical beams and gir- 
ders, stiffness of, 181 
— strength of, 170 

— boiler with fines, 255 

— wrought-iron columns, 

203 



FOU 

DEFLECTION and 
strength, constants 
of, 176 
— of columns, 198 
Double riveting, 247 
Dry mould, cast iron in, 35 



EDGES, knife, 17 
Effect of lead and 
tin in brass, 88 

— of repeated deflection on 

cast iron, 128 

temperature, 249 

Elastic flexibility, 13 
Elasticity, 3 

— of aeriform bodies, 5 

— an advantage, 7 

— Hooke's law of, 4 

— imperfect, 4 

— limit of, 9, 11, 12, 22 

— of cast iron, 12, 38, 128 

copper and tin, 12 

hard steel, 12 

— — liquids, 5 

plastic materials, 5 

solids, 6, 7 

watch-spring, 5 

wrought iron, 61 

— perfect, 3, 4, 5, 11, 12 

— used up, 7 

Elliptical tubes, collapse 

of, 269 
Elm timber, 109 
Examples of constants, 

174, t-75 
Expansion and contraction 

in boilers, 250 
Experiments, collapse of 

butt joints, 267 
overlap joints, 267 

— Fairbairn's, 263 

— of Railway Commission, 

11, 22 

— with aluminium bronze, 

97 

bending bar, 28 

cast iron, 38, 39 

Extension at weak point, 7 



FLANGED cantilevers, 
173 

Flexible beam made rigid, 8 
Flexure of columns, 198 
Fluidity of cast iron, 35 
Fluxes of cast iron, 30 
Forces, triangle of, 208 
Formulae, 158 . 
Foundation, cast-iron cy- 
linder, 232 

— centre support of, 236 

— concrete, 230, 232 



GIR 

Foun dation— e<?«/. 

— corner piles, 238, 239, 

240 

— diagrams of, 231, 233, 

2 34> 235, 237, 240 

— distribution of weight.. 

238 

— for pier head, 232 
solid wharf, 230 

— holding down bolts, 230 

— piles for, 238 

— pressure on vertical 

struts, 238 

— resistance to counter- 

balance weight, 230 

— struts, stress on, 236 

— surrounding piles, 23C 

— upper tier girders, 235 
Frictional resistance of 

joints, 244 
Fusibility of brass, 88 



GEARING, overhung 
bearing, 185 

— strength of, 187 
Girder, cast-iron, 35, 167 

— considered as a canti- 

lever, 161 

lever, 161 

practically, 165 

■ — deflection of, 180, 182 
examples of, 182, 183, 



— — when uniformly load- 

ed, 182 

— disposal of material in, 

165 • 

— experiments on, by 

Hodgkinson, 179 

— flanged, 167, 169, 177 

deflection of, 180 

strains of, 177 

— neutral axis of section, 

166 

— resilience of, 186 

— semi, deflection of, 181 

— square and round tube, 

strength of, 171 

— stiffness of, 181 

— strength of, 160 

— stress on, 168 

— tubular, 159 

— under different condi- 

tions, 162, 163, 164 
Girders and beams, 157, 

J 5.9 

— cylindrical, stiffness of, 

181 
strength of, 170 

— of uniform strength, 

172 

— rectangular, deflection 

of, 180 



GIR 

Girders and beams— cont. 

— rectangular, stiffness of, 

181 
strongest form of, 170 

— rigid, 8 j r 

— secure fixing at ends ct, 

160 

— square, strength of, 170 

— stiffness of, 1S1 
Guns, cast-iron, 32 

Gun construction, by build- 
ing up, 282 

— strength depending on 

outward form, 279 

— grip of hoops, 286 

— homogeneity, 283 

— inner barrel, 285 

— lining cast-iron gun, 290 

— 1 mgitudinal strain, 28'^ 

— Paliiser and Parsons, 

290 

— principles of, applicable 

to other structures, 
292 

— shrinking, system of, 

284 

— slow cooling, 278 

— stress on hoops, 286 

— the breech, 289 

— theory of lining, 291 
— ■ us; of vernier, 287 

— water core, 278 

— wrought-iron hoops, 283 
Gun-metal (see bronze) 



HARDNESS and brit- 
tleness, 12 
Hornbeam timber, no 
Hydraulic crane, 210 
diagrams of stress, 

211 

jib of, 211 

stress on component 

parts of, 212 

post of, 211 

— cylinders, 279 



TMPACT, 125 

J. — cast iron under, 45 

— deflection due to, 126 

— effect of, on cast iron, 

125 _ 

— experiments on, 125 

— sets under, 126 

— vertical, 126 
Impurity, cast iron ex- 
posed to, 31 

Instrument for testing ma- 
terials, 2 
Internal flue, 250 

— pressure, experiments 

on, 270 



Index. 

NAT 

Iron, cast (see cast-iron) 
— wrought (see wrought- 
iron) 



JOINTS, riveted, con- 
struction of, 243 

— diagonal, 247 

— frictional resistance of, 

244 

— lap and butt, 267 

— strength of, 241, 247 



T^NIFE-EDGES, 17 



299 



SCR 



L 



IQUID CAST IRON, 



31 
Lap joints, 267 



MACHINERY, air 
and water, 6 
Mahogany, in 
Material, 2 

— constructive value of, 1 

— endurance of, 1 

— fitness of, 1 

— for boilers, 249 

— instruments for testing, 

2 

— permanence of form, 2 

— reliability of, 1 

— rigidity of, 2 

— ■ soft and ductile, 22 

— stretching of, 3 
Metal, Babbitt's, 98 

— bell, q8 

preservation of, 98 

— ductile, 27 

— flow of, 23, 26, 27, 28 

— specific gravity of, 27 

— malleable, 27 

— melting point of, 99 

— resistance to compres- 

sion, 100 

tension, 100 

Muntz-metal, 89 

— for guns, 89 

— strength of, 89 



NATURAL PRINCI- 
PLES, 293 

— approximately complied 

with, 293 

— in grinding, 295 

steam engine, 295 

tools, 294 

— underlying mechanical 

operations, 296 



OAK TIMBER, m 
Ore of cast iron, re- 
fractory, 30 
Overhead travelling crane, 
209 



PARABOLIC CO- 
LUMNS, 199 
Permanent elongation of 
cast iron, 37 

— set, 10 

of cast iron, 33, 38, 

39 
Pine and fir, no 
Pinion, wear of, 190 
Pipes, cast-iron, 271 

— high pressure, 273 
strength of, 273 

— strength of, 272 
Planks, behaviour of, 106 
Plate and joint, relative 

strength of, 244 
Plates, arrangement of, in 
boiler, 241 

— strength of, 241 

— thickness at edges, 247 
Power transmitted by 

wheels, 191 
Proof strains of chains, 153 
Punching and drilling, 145 

— careless, 247 

— experiments on, 146 

— resistance to, 144 

— stress, 145 



REMELTING OF 
CAST IRON, 44 
Rigidity of cast iron, 35 
Rivet, elongated, 245 
Riveted structures, 241 
Rivets, strength of, 241 
Roof-truss, strength of, 207 
Ropes, experiments with, 
156 

— strength of, 155 
Rectangular beams and 

girders, strongest form 

of, 170 

deflection of, 180 

stiffness of, 181 

— wrought-iron columns, 

202 
Rules for strength of 
chains, 153 



CCREW BOLT, 
O strength of, 150 
Screws, square threaded, 

193 
— strength of, 192 



too 



Index. 



SCR 

Screws, strength ol—cont. 

angular thread, 192 

round top and bot- 
tom, 193 

— thread of, right-angled 

triangle, 193 
Shafts, 134 

— cast-iron, 132 

— correct proportions of, 

135 ,_ r 

— crane, strength of, 139 

— diameter of, 134 

— elasticity of, 136 

— engine, expansive, 141 

— hollow, strength of, 131 

— stiffness of, 143, 134, 

— strength of, 131, 134, 137, 

i39 . 

— wrought-iron, 132 
Shearing and punching, 143 

— detrusion, 144 

— effect of, 144 

— experiments on, 148 

— resistance to, 144 

— stress, 145 
Sheer-poles (or legs), 212 

— diagram of, 213 

— guy chains of, 214 

— steel, 204 

— strength of, 212 

— stress on guys, 214 

— strength of, 205 
Sheer-pole tackles, 215 
Shell, chilled, 281 
Solids, elasticity of, 6, 7 
Specific gravity of brass, S8 

• cast iron, 27 

wrought iron after 

compress on, 67 
Specimen bridles, 20 

— each part of, independ- 

ent, 10 

— elongation of, per ton, 

21 

— holder for punching, 24 
transverse resist- 
ance, 24 

Specimens for compression, 

14 

extension, 13 

testing, 9 

— long and short, 9, 37 

— prepared in lathe, 13, 28 

— rupture of, 19 

— sketch of, 19, 21 

— unequal stretching of, 9 
Spiegel-Eisen, 69 
Springs, railway carriage, 8 

— steel, 5 

— watch, elasticity of, 5 
Steam crane, centre pivot, 

215, 221, 222 

— deviation of pressures, 

217 



STR 

Steam crane — cont. 

— diagrams of, 216, 217, 

219, 225 

— for 30-tons load, 215 

— girders, strength of, 223 

— jib, construction of, 218, 

219 

— pinion overhung, 228 

— pressure on guide rail, 

217 

— side frames, 224, 225 

— strain on centre pivot, 

218 

chain, 229 

guide rail, 236 

jib and tension 

rods, 218, 221 

— strength of shafts, 226 

— stress on guide-wheel 

shaft, 227 

■ — side frames, 226 

Steel, 68 

— Bessemer, 69, 76 

— cementation, 68 

— compression of, 76 

— determination of 

strength, 73 

— effect of tempering, 73 

— elasticity of, 71 

— for rough structures, 72 

— goodness of, 71 

— gun, 71 

— in testing machine, 75 

— — large masses, 69 

— percentage of carbon in, 

67 

— porosity of, 70 

— related to cast iron, 68 

— tempered in oil, 72 

— tenacity of, 73 

— testing of, 72 

— testing gun blocks of, 

74 

— Whitworth's treatment 

of, 70 
Sterro-metal, 90 

— composition of, 90 

— compressibility of, 91 

— experiments with, 90, 

92, 93 

— tenacity of, 91 
Strength and deflection, 

constants of, 176 

— of boilers, 253, 256 

cast iron, 32, 34, 45 

chains, rules for, 154 

columns depending 

on fixing, 196, 197 
columns, long and 

short, 195 

plates, 241 

square beams and 

girders, 170 
rivets, 241 



TIM 

Strength— cont. 

— surplus, effect of, 150 

— torsional, 27 

Stress in proportion to 
stretch, 277 

— limit of, 11 

— on 50-feet bar, 11 
joints, 257 

— theory of, 276 
Structures, complex, 

strength of, 206 

— hooped and solid, 276 

— riveted, 241 



TANKS, cast-iron, 273 
— hooped, 275 

— strength of, 274 
Teak timber, 112 
Temperature, dependence 

of cast iron on, 44 
Tenacity of brass, 89 

cast iron, 34 

Tensile strength of brass, 

89 

cast iron, 33 

Test bars of cast iron, 36 

— beam of cast iron, 37 
Tests of cast iron, 36 
Testing boilers, 251 

— bridles, 17 

— by gauge, 21 

impact, 12 

lever, 15 

torsion, 26 

— care necessary in, 18 

— cast iron by hydraulic 

press, 36 

— Machine, 10, 12 

adjustment of, 19, 26 

American, 15 

balance of, 17 

cast iron in, 32 

compound lever, 14 

compression by, 23 

lever, 14 

simple, 29 

single lever, 14 

strength of, 13 

Woolwich, 14, 16 

— rectangular bars, 25 

— ten-feet bars of cast iron, 

.37 

— time an important ele- 

ment in, 10 

— weights, 18 

Thrust on triangular struc- 
ture, 208 
Tie beam, 159 

— rods, 8 
Timber, 101 

— age of, 102 

— ash, 10S 



Index. 



301 



TIM 

Timber — cont. 

— beams, strength of, 121 

— beech, 109 

— change in form of, 104 

— commercial value of, 102 

— density of, 102 

— elm, 109 

— hornbeam, no 

— mahogany, in_ 

— medullary rays in, 104 

— oak, in 

— pine and fir, no 

— resistance to crushing, 

114, "5 

— seasoning of, 103 

— shearing of, 116 

— shrinking of, 103 

— strength of, 102 

— teak, 112 

— tenacity of, 113 

— transverse strength of, 

117 

— under compression, 115 
Torsion and shearing, 130, 

i37 

— experiments on, 132, 135 

— resistance to, 131 
Torsional elasticity, 133 

— stiffness, 133 

— strength, 27 

of cast steel, 133 

: — copper, 133 

■ — shafting, 131 

wrought iron, 131 

Transverse flexure, experi- 
ments on, 127 

— strength, experiments 

on, 123 

of iron, 122 

ratio of, 125 

Travelling crane, overhead, 

209 
Triangle of forces, 208 
Trussed beam, counter- 
braces, 210 

diagram of, 209 

movable load of, 209 

stress of, 209 

Tube boilers, small, 270 

— circular, collapse of, 267 

— elliptical, collapse of, 269 
Tubular boilers, 257, 258 

fire-box of, 260 

smoke-box of, 261 

stays of, 260 

strength of, 258 



WRO 

UNDER-GIRDERS, 
conditions of load, 
160 
Uniformity of sectional area 
of screw bolt, 149, 150 

section in chains, 152 

Uniform strength of beams 

and girders, 172 
Use of constants, 173 



WATCH-SPRING, 
elasticity of, 5 
Water, elastic, 6 
Wheels for transmitting 

power, 191 
Wheel teeth of, 187 

adjustment of, 189 

cast-iron, 188, 190 

examples of, 189 

malleable cast-iron, 

191 

steel, 191 

strength of, 188 

■ wrought-iron, 191 

Wires, bundle of, 28 
Wrought-iron, 28, 46 

— affected by temperature, 

5° 

— annealing, 52, 67 

— appearance of fracture, 

S 1 

— behaviour of, 54 

— broken suddenly, 51 

— butt-welding, 56 

— bulging, 67 

— carbon, percentage of, 

4 8 

— care required in manu- 

facture, 47 

— cementation of, 47 

— chains, 52 

— change from cast iron, 

46 

— cold rolling, 49 

— cold-short, 53 

— columns, 202 

— compared with cast iron, 

39, 54 

— compression of, 40 

— conditions for welding, 

— deflection of, 67 

— difference in quality of, 

47 



WRO 

Wrought-iron — cont. 

— ductile property of, 52 

— effect of overheating, 49 
of time on, 61 

— elasticity of, 61 

— elastic limit of, 47 

— equilibrium in, 29 

— experiments with, 56 
for compression, 

64 

50-feet bars, 57 

to 63 

— extension of, 61 

— fibre of, 28, 50 

— for columns, 204 

— forging of, 48 

— fracture of, 52 

— hard and soft, 55 

— in bar, 49, 56 
cylinder, 56 

— loss of strength of, 56 

— made with charcoal, 47 

— malleable, 46 

— mechanical impurities 

of, 47 

— modulus of elasticity, 62 

— permanent set of, 54, 

62 

— piling, 47 

— puddling of, 46 

— purity of welding sur- 

face of, 49 

— rectangular columns, 202 

— red-short, 53 

— rigidity of, 53 

— rolling of, 47 

— safe load for, 53 

— scarf joints, 56 

— soft, 48 

— specific gravity of, after 

compression, 67V 

— steely, 49 

— strength at right anglei 

to fibre, 50 
of, 47, 50, 204 

— strength of thin plates, 5 
welds, 56 

— testing for hardness of, 

48 

— ultimate strength of, 

4 9 

— under compression, 63 

— unlike wood, 28 

— welding of, 46 

— when turned, 49 

— wire-drawn, 54 



WORKS 



JOIN TYIDALL, LL.D. E.E.S. 

Professor of Natural Philosophy 
in the Royal Institution of Great Britain. 



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